id	sid	tid	token	lemma	pos
ejpam-1480	1	1	6_137723_parsa.dvi	6_137723_parsa.dvi	NUM
ejpam-1480	1	2	european	european	PROPN
ejpam-1480	1	3	journal	journal	PROPN
ejpam-1480	1	4	of	of	ADP
ejpam-1480	1	5	pure	pure	ADJ
ejpam-1480	1	6	and	and	CCONJ
ejpam-1480	1	7	applied	apply	VERB
ejpam-1480	1	8	mathematics	mathematic	NOUN
ejpam-1480	1	9	vol	vol	NOUN
ejpam-1480	1	10	.	.	PROPN
ejpam-1480	1	11	5	5	NUM
ejpam-1480	1	12	,	,	PUNCT
ejpam-1480	1	13	no	no	INTJ
ejpam-1480	1	14	.	.	NOUN
ejpam-1480	1	15	1	1	NUM
ejpam-1480	1	16	,	,	PUNCT
ejpam-1480	1	17	2012	2012	NUM
ejpam-1480	1	18	,	,	PUNCT
ejpam-1480	1	19	55	55	NUM
ejpam-1480	1	20	-	-	SYM
ejpam-1480	1	21	58	58	NUM
ejpam-1480	1	22	issn	issn	PROPN
ejpam-1480	1	23	1307	1307	NUM
ejpam-1480	1	24	-	-	SYM
ejpam-1480	1	25	5543	5543	NUM
ejpam-1480	1	26	–	–	PUNCT
ejpam-1480	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1480	1	28	special	special	ADJ
ejpam-1480	1	29	issue	issue	NOUN
ejpam-1480	1	30	for	for	ADP
ejpam-1480	1	31	the	the	DET
ejpam-1480	1	32	international	international	ADJ
ejpam-1480	1	33	conference	conference	NOUN
ejpam-1480	1	34	on	on	ADP
ejpam-1480	1	35	applied	apply	VERB
ejpam-1480	1	36	analysis	analysis	NOUN
ejpam-1480	1	37	and	and	CCONJ
ejpam-1480	1	38	algebra	algebra	NOUN
ejpam-1480	1	39	29	29	NUM
ejpam-1480	1	40	june	june	PROPN
ejpam-1480	1	41	02	02	NUM
ejpam-1480	1	42	july	july	PROPN
ejpam-1480	1	43	2011	2011	NUM
ejpam-1480	1	44	,	,	PUNCT
ejpam-1480	1	45	istanbul	istanbul	PROPN
ejpam-1480	1	46	turkey	turkey	PROPN
ejpam-1480	1	47	on	on	ADP
ejpam-1480	1	48	the	the	DET
ejpam-1480	1	49	vanishing	vanish	VERB
ejpam-1480	1	50	properties	property	NOUN
ejpam-1480	1	51	of	of	ADP
ejpam-1480	1	52	local	local	ADJ
ejpam-1480	1	53	cohomology	cohomology	NOUN
ejpam-1480	1	54	modules	module	NOUN
ejpam-1480	1	55	defined	define	VERB
ejpam-1480	1	56	by	by	ADP
ejpam-1480	1	57	a	a	DET
ejpam-1480	1	58	pair	pair	NOUN
ejpam-1480	1	59	of	of	ADP
ejpam-1480	1	60	ideals	ideal	NOUN
ejpam-1480	1	61	m.	m.	NOUN
ejpam-1480	1	62	lotfi	lotfi	PROPN
ejpam-1480	1	63	parsa,∗	parsa,∗	NOUN
ejpam-1480	1	64	,	,	PUNCT
ejpam-1480	1	65	sh	sh	PROPN
ejpam-1480	1	66	.	.	PROPN
ejpam-1480	1	67	payrovi	payrovi	PROPN
ejpam-1480	1	68	department	department	PROPN
ejpam-1480	1	69	of	of	ADP
ejpam-1480	1	70	mathematics	mathematics	PROPN
ejpam-1480	1	71	,	,	PUNCT
ejpam-1480	1	72	i.	i.	PROPN
ejpam-1480	1	73	k.	k.	PROPN
ejpam-1480	2	1	international	international	PROPN
ejpam-1480	2	2	university	university	PROPN
ejpam-1480	2	3	,	,	PUNCT
ejpam-1480	2	4	qazvin	qazvin	ADV
ejpam-1480	2	5	,	,	PUNCT
ejpam-1480	2	6	iran	iran	PROPN
ejpam-1480	2	7	abstract	abstract	NOUN
ejpam-1480	2	8	.	.	PUNCT
ejpam-1480	3	1	as	as	ADP
ejpam-1480	3	2	a	a	DET
ejpam-1480	3	3	generalization	generalization	NOUN
ejpam-1480	3	4	of	of	ADP
ejpam-1480	3	5	the	the	DET
ejpam-1480	3	6	ordinary	ordinary	ADJ
ejpam-1480	3	7	local	local	ADJ
ejpam-1480	3	8	cohomology	cohomology	NOUN
ejpam-1480	3	9	modules	module	NOUN
ejpam-1480	3	10	,	,	PUNCT
ejpam-1480	3	11	recently	recently	ADV
ejpam-1480	3	12	some	some	DET
ejpam-1480	3	13	authors	author	NOUN
ejpam-1480	3	14	introduced	introduce	VERB
ejpam-1480	3	15	the	the	DET
ejpam-1480	3	16	local	local	ADJ
ejpam-1480	3	17	cohomology	cohomology	NOUN
ejpam-1480	3	18	modules	module	NOUN
ejpam-1480	3	19	with	with	ADP
ejpam-1480	3	20	respect	respect	NOUN
ejpam-1480	3	21	to	to	ADP
ejpam-1480	3	22	a	a	DET
ejpam-1480	3	23	pair	pair	NOUN
ejpam-1480	3	24	of	of	ADP
ejpam-1480	3	25	ideals	ideal	NOUN
ejpam-1480	3	26	.	.	PUNCT
ejpam-1480	4	1	in	in	ADP
ejpam-1480	4	2	this	this	DET
ejpam-1480	4	3	paper	paper	NOUN
ejpam-1480	4	4	,	,	PUNCT
ejpam-1480	4	5	we	we	PRON
ejpam-1480	4	6	get	get	VERB
ejpam-1480	4	7	some	some	DET
ejpam-1480	4	8	results	result	NOUN
ejpam-1480	4	9	on	on	ADP
ejpam-1480	4	10	artinianness	artinianness	ADJ
ejpam-1480	4	11	,	,	PUNCT
ejpam-1480	4	12	vanishing	vanishing	NOUN
ejpam-1480	4	13	,	,	PUNCT
ejpam-1480	4	14	finiteness	finiteness	NOUN
ejpam-1480	4	15	and	and	CCONJ
ejpam-1480	4	16	other	other	ADJ
ejpam-1480	4	17	properties	property	NOUN
ejpam-1480	4	18	of	of	ADP
ejpam-1480	4	19	these	these	DET
ejpam-1480	4	20	modules	module	NOUN
ejpam-1480	4	21	.	.	PUNCT
ejpam-1480	5	1	let	let	VERB
ejpam-1480	5	2	r	r	PRON
ejpam-1480	5	3	be	be	AUX
ejpam-1480	5	4	a	a	DET
ejpam-1480	5	5	commutative	commutative	ADJ
ejpam-1480	5	6	noetherian	noetherian	ADJ
ejpam-1480	5	7	ring	ring	NOUN
ejpam-1480	5	8	,	,	PUNCT
ejpam-1480	5	9	i	i	PRON
ejpam-1480	5	10	,	,	PUNCT
ejpam-1480	5	11	j	j	PROPN
ejpam-1480	5	12	two	two	NUM
ejpam-1480	5	13	ideals	ideal	NOUN
ejpam-1480	5	14	of	of	ADP
ejpam-1480	5	15	r	r	NOUN
ejpam-1480	5	16	and	and	CCONJ
ejpam-1480	5	17	m	m	VERB
ejpam-1480	5	18	a	a	DET
ejpam-1480	5	19	finitely	finitely	ADV
ejpam-1480	5	20	generated	generate	VERB
ejpam-1480	5	21	r	r	NOUN
ejpam-1480	5	22	-	-	PUNCT
ejpam-1480	5	23	module	module	NOUN
ejpam-1480	5	24	such	such	ADJ
ejpam-1480	5	25	that	that	DET
ejpam-1480	5	26	dimr	dimr	NOUN
ejpam-1480	5	27	m	m	PROPN
ejpam-1480	5	28	=	=	NOUN
ejpam-1480	6	1	n.	n.	NOUN
ejpam-1480	6	2	we	we	PRON
ejpam-1480	6	3	prove	prove	VERB
ejpam-1480	6	4	that	that	SCONJ
ejpam-1480	6	5	hn	hn	PROPN
ejpam-1480	6	6	i	i	PROPN
ejpam-1480	6	7	,	,	PUNCT
ejpam-1480	6	8	j	j	PROPN
ejpam-1480	6	9	(	(	PUNCT
ejpam-1480	6	10	m)/jhn	m)/jhn	PROPN
ejpam-1480	6	11	i	i	PROPN
ejpam-1480	6	12	,	,	PUNCT
ejpam-1480	6	13	j	j	PROPN
ejpam-1480	6	14	(	(	PUNCT
ejpam-1480	6	15	m	m	PROPN
ejpam-1480	6	16	)	)	PUNCT
ejpam-1480	6	17	is	be	AUX
ejpam-1480	6	18	i	i	PRON
ejpam-1480	6	19	-cofinite	-cofinite	ADJ
ejpam-1480	6	20	artinian	artinian	ADJ
ejpam-1480	6	21	and	and	CCONJ
ejpam-1480	7	1	hn	hn	PROPN
ejpam-1480	7	2	i	i	PROPN
ejpam-1480	7	3	,	,	PUNCT
ejpam-1480	7	4	j	j	PROPN
ejpam-1480	7	5	(	(	PUNCT
ejpam-1480	7	6	m)/ihn	m)/ihn	PROPN
ejpam-1480	7	7	i	i	PROPN
ejpam-1480	7	8	,	,	PUNCT
ejpam-1480	7	9	j	j	PROPN
ejpam-1480	7	10	(	(	PUNCT
ejpam-1480	7	11	m	m	PROPN
ejpam-1480	7	12	)	)	PUNCT
ejpam-1480	7	13	has	have	VERB
ejpam-1480	7	14	finite	finite	ADJ
ejpam-1480	7	15	length	length	NOUN
ejpam-1480	7	16	.	.	PUNCT
ejpam-1480	8	1	also	also	ADV
ejpam-1480	8	2	we	we	PRON
ejpam-1480	8	3	show	show	VERB
ejpam-1480	8	4	that	that	SCONJ
ejpam-1480	8	5	,	,	PUNCT
ejpam-1480	8	6	if	if	SCONJ
ejpam-1480	8	7	r	r	NOUN
ejpam-1480	8	8	is	be	AUX
ejpam-1480	8	9	local	local	ADJ
ejpam-1480	8	10	with	with	ADP
ejpam-1480	8	11	dim	dim	ADJ
ejpam-1480	8	12	r	r	NOUN
ejpam-1480	8	13	/	/	SYM
ejpam-1480	8	14	i	i	PROPN
ejpam-1480	8	15	+	+	NUM
ejpam-1480	8	16	j	j	PROPN
ejpam-1480	8	17	=	=	SYM
ejpam-1480	8	18	0	0	NUM
ejpam-1480	8	19	and	and	CCONJ
ejpam-1480	8	20	dimr	dimr	NOUN
ejpam-1480	8	21	m	m	PROPN
ejpam-1480	8	22	/	/	SYM
ejpam-1480	8	23	j	j	PROPN
ejpam-1480	8	24	m	m	NOUN
ejpam-1480	8	25	=	=	SYM
ejpam-1480	9	1	d	d	X
ejpam-1480	9	2	>	>	X
ejpam-1480	9	3	0	0	PROPN
ejpam-1480	9	4	,	,	PUNCT
ejpam-1480	9	5	then	then	ADV
ejpam-1480	9	6	hd	hd	VERB
ejpam-1480	9	7	i	i	PROPN
ejpam-1480	9	8	,	,	PUNCT
ejpam-1480	9	9	j	j	PROPN
ejpam-1480	9	10	(	(	PUNCT
ejpam-1480	9	11	m	m	PROPN
ejpam-1480	9	12	)	)	PUNCT
ejpam-1480	9	13	is	be	AUX
ejpam-1480	9	14	not	not	PART
ejpam-1480	9	15	finitely	finitely	ADV
ejpam-1480	9	16	generated	generate	VERB
ejpam-1480	9	17	.	.	PUNCT
ejpam-1480	10	1	2000	2000	NUM
ejpam-1480	10	2	mathematics	mathematic	NOUN
ejpam-1480	10	3	subject	subject	NOUN
ejpam-1480	10	4	classifications	classification	NOUN
ejpam-1480	10	5	:	:	PUNCT
ejpam-1480	10	6	13d45	13d45	NUM
ejpam-1480	10	7	,	,	PUNCT
ejpam-1480	10	8	13e05	13e05	NUM
ejpam-1480	10	9	,	,	PUNCT
ejpam-1480	10	10	13e10	13e10	NUM
ejpam-1480	10	11	.	.	PUNCT
ejpam-1480	11	1	key	key	ADJ
ejpam-1480	11	2	words	word	NOUN
ejpam-1480	11	3	and	and	CCONJ
ejpam-1480	11	4	phrases	phrase	NOUN
ejpam-1480	11	5	:	:	PUNCT
ejpam-1480	11	6	artinian	artinian	ADJ
ejpam-1480	11	7	module	module	NOUN
ejpam-1480	11	8	,	,	PUNCT
ejpam-1480	11	9	cofinite	cofinite	NOUN
ejpam-1480	11	10	module	module	NOUN
ejpam-1480	11	11	,	,	PUNCT
ejpam-1480	11	12	local	local	ADJ
ejpam-1480	11	13	cohomology	cohomology	NOUN
ejpam-1480	11	14	,	,	PUNCT
ejpam-1480	11	15	noetherian	noetherian	ADJ
ejpam-1480	11	16	module	module	NOUN
ejpam-1480	11	17	.	.	PUNCT
ejpam-1480	12	1	1	1	X
ejpam-1480	12	2	.	.	X
ejpam-1480	12	3	introduction	introduction	NOUN
ejpam-1480	12	4	throughout	throughout	ADP
ejpam-1480	12	5	this	this	DET
ejpam-1480	12	6	paper	paper	NOUN
ejpam-1480	12	7	,	,	PUNCT
ejpam-1480	12	8	r	r	NOUN
ejpam-1480	12	9	is	be	AUX
ejpam-1480	12	10	a	a	DET
ejpam-1480	12	11	commutative	commutative	ADJ
ejpam-1480	12	12	noetherian	noetherian	ADJ
ejpam-1480	12	13	ring	ring	NOUN
ejpam-1480	12	14	with	with	ADP
ejpam-1480	12	15	non	non	ADJ
ejpam-1480	12	16	-	-	ADJ
ejpam-1480	12	17	zero	zero	NUM
ejpam-1480	12	18	identity	identity	NOUN
ejpam-1480	12	19	,	,	PUNCT
ejpam-1480	12	20	i	i	PRON
ejpam-1480	12	21	,	,	PUNCT
ejpam-1480	12	22	j	j	PROPN
ejpam-1480	12	23	are	be	AUX
ejpam-1480	12	24	two	two	NUM
ejpam-1480	12	25	ideals	ideal	NOUN
ejpam-1480	12	26	of	of	ADP
ejpam-1480	12	27	r	r	NOUN
ejpam-1480	12	28	and	and	CCONJ
ejpam-1480	12	29	m	m	PROPN
ejpam-1480	12	30	is	be	AUX
ejpam-1480	12	31	an	an	DET
ejpam-1480	12	32	r	r	NOUN
ejpam-1480	12	33	-	-	PUNCT
ejpam-1480	12	34	module	module	NOUN
ejpam-1480	12	35	.	.	PUNCT
ejpam-1480	13	1	for	for	ADP
ejpam-1480	13	2	notations	notation	NOUN
ejpam-1480	13	3	and	and	CCONJ
ejpam-1480	13	4	terminologies	terminology	NOUN
ejpam-1480	13	5	not	not	PART
ejpam-1480	13	6	given	give	VERB
ejpam-1480	13	7	in	in	ADP
ejpam-1480	13	8	this	this	DET
ejpam-1480	13	9	paper	paper	NOUN
ejpam-1480	13	10	,	,	PUNCT
ejpam-1480	13	11	the	the	DET
ejpam-1480	13	12	reader	reader	NOUN
ejpam-1480	13	13	is	be	AUX
ejpam-1480	13	14	referred	refer	VERB
ejpam-1480	13	15	to	to	ADP
ejpam-1480	13	16	[	[	X
ejpam-1480	13	17	1	1	NUM
ejpam-1480	13	18	]	]	PUNCT
ejpam-1480	13	19	and	and	CCONJ
ejpam-1480	13	20	[	[	X
ejpam-1480	13	21	6	6	NUM
ejpam-1480	13	22	]	]	PUNCT
ejpam-1480	13	23	,	,	PUNCT
ejpam-1480	13	24	if	if	SCONJ
ejpam-1480	13	25	necessary	necessary	ADJ
ejpam-1480	13	26	.	.	PUNCT
ejpam-1480	14	1	as	as	ADP
ejpam-1480	14	2	a	a	DET
ejpam-1480	14	3	generalization	generalization	NOUN
ejpam-1480	14	4	of	of	ADP
ejpam-1480	14	5	the	the	DET
ejpam-1480	14	6	ordinary	ordinary	ADJ
ejpam-1480	14	7	local	local	ADJ
ejpam-1480	14	8	cohomology	cohomology	NOUN
ejpam-1480	14	9	modules	module	NOUN
ejpam-1480	14	10	,	,	PUNCT
ejpam-1480	14	11	takahashi	takahashi	PROPN
ejpam-1480	14	12	,	,	PUNCT
ejpam-1480	14	13	yoshino	yoshino	NOUN
ejpam-1480	14	14	and	and	CCONJ
ejpam-1480	14	15	yoshizawa	yoshizawa	PROPN
ejpam-1480	14	16	,	,	PUNCT
ejpam-1480	14	17	in	in	ADP
ejpam-1480	14	18	[	[	PUNCT
ejpam-1480	14	19	6	6	NUM
ejpam-1480	14	20	]	]	PUNCT
ejpam-1480	14	21	,	,	PUNCT
ejpam-1480	14	22	introduced	introduce	VERB
ejpam-1480	14	23	the	the	DET
ejpam-1480	14	24	local	local	ADJ
ejpam-1480	14	25	cohomology	cohomology	NOUN
ejpam-1480	14	26	modules	module	NOUN
ejpam-1480	14	27	with	with	ADP
ejpam-1480	14	28	respect	respect	NOUN
ejpam-1480	14	29	to	to	ADP
ejpam-1480	14	30	a	a	DET
ejpam-1480	14	31	pair	pair	NOUN
ejpam-1480	14	32	of	of	ADP
ejpam-1480	14	33	ideals	ideal	NOUN
ejpam-1480	14	34	(	(	PUNCT
ejpam-1480	14	35	i	i	PROPN
ejpam-1480	14	36	,	,	PUNCT
ejpam-1480	14	37	j	j	PROPN
ejpam-1480	14	38	)	)	PUNCT
ejpam-1480	14	39	.	.	PUNCT
ejpam-1480	15	1	to	to	PART
ejpam-1480	15	2	be	be	AUX
ejpam-1480	15	3	more	more	ADV
ejpam-1480	15	4	precise	precise	ADJ
ejpam-1480	15	5	,	,	PUNCT
ejpam-1480	15	6	let	let	VERB
ejpam-1480	15	7	w(i	w(i	PROPN
ejpam-1480	15	8	,	,	PUNCT
ejpam-1480	15	9	j	j	PROPN
ejpam-1480	15	10	)	)	PUNCT
ejpam-1480	15	11	=	=	PRON
ejpam-1480	15	12	{	{	PUNCT
ejpam-1480	15	13	p	p	NOUN
ejpam-1480	15	14	∈	∈	PROPN
ejpam-1480	15	15	spec(r	spec(r	PROPN
ejpam-1480	15	16	)	)	PUNCT
ejpam-1480	15	17	:	:	PUNCT
ejpam-1480	16	1	i	i	PRON
ejpam-1480	16	2	t	t	VERB
ejpam-1480	16	3	⊆	⊆	NUM
ejpam-1480	16	4	p+	p+	PROPN
ejpam-1480	16	5	j	j	NOUN
ejpam-1480	16	6	for	for	ADP
ejpam-1480	16	7	some	some	DET
ejpam-1480	16	8	positive	positive	ADJ
ejpam-1480	16	9	integer	integer	NOUN
ejpam-1480	16	10	t	t	PROPN
ejpam-1480	16	11	}	}	PUNCT
ejpam-1480	16	12	.	.	PUNCT
ejpam-1480	17	1	the	the	DET
ejpam-1480	17	2	set	set	NOUN
ejpam-1480	17	3	of	of	ADP
ejpam-1480	17	4	elements	element	NOUN
ejpam-1480	17	5	x	x	PUNCT
ejpam-1480	17	6	of	of	ADP
ejpam-1480	17	7	m	m	PRON
ejpam-1480	17	8	such	such	ADJ
ejpam-1480	17	9	that	that	SCONJ
ejpam-1480	17	10	supprrx	supprrx	NOUN
ejpam-1480	17	11	⊆w(i	⊆w(i	NOUN
ejpam-1480	17	12	,	,	PUNCT
ejpam-1480	17	13	j	j	PROPN
ejpam-1480	17	14	)	)	PUNCT
ejpam-1480	17	15	,	,	PUNCT
ejpam-1480	17	16	is	be	AUX
ejpam-1480	17	17	said	say	VERB
ejpam-1480	17	18	to	to	PART
ejpam-1480	17	19	be	be	AUX
ejpam-1480	17	20	(	(	PUNCT
ejpam-1480	17	21	i	i	NOUN
ejpam-1480	17	22	,	,	PUNCT
ejpam-1480	17	23	j)-torsion	j)-torsion	PROPN
ejpam-1480	17	24	submodule	submodule	NOUN
ejpam-1480	17	25	of	of	ADP
ejpam-1480	17	26	m	m	PRON
ejpam-1480	17	27	and	and	CCONJ
ejpam-1480	17	28	is	be	AUX
ejpam-1480	17	29	denoted	denote	VERB
ejpam-1480	17	30	by	by	ADP
ejpam-1480	17	31	γi	γi	PROPN
ejpam-1480	17	32	,	,	PUNCT
ejpam-1480	17	33	j(m	j(m	PROPN
ejpam-1480	17	34	)	)	PUNCT
ejpam-1480	17	35	.	.	PUNCT
ejpam-1480	18	1	it	it	PRON
ejpam-1480	18	2	is	be	AUX
ejpam-1480	18	3	easy	easy	ADJ
ejpam-1480	18	4	to	to	PART
ejpam-1480	18	5	see	see	VERB
ejpam-1480	18	6	that	that	PRON
ejpam-1480	18	7	γi	γi	PROPN
ejpam-1480	18	8	,	,	PUNCT
ejpam-1480	18	9	j	j	PROPN
ejpam-1480	18	10	is	be	AUX
ejpam-1480	18	11	a	a	DET
ejpam-1480	18	12	covariant	covariant	NOUN
ejpam-1480	18	13	,	,	PUNCT
ejpam-1480	18	14	r	r	NOUN
ejpam-1480	18	15	-	-	PUNCT
ejpam-1480	18	16	linear	linear	NOUN
ejpam-1480	18	17	functor	functor	NOUN
ejpam-1480	18	18	from	from	ADP
ejpam-1480	18	19	the	the	DET
ejpam-1480	18	20	category	category	NOUN
ejpam-1480	18	21	of	of	ADP
ejpam-1480	18	22	r	r	NOUN
ejpam-1480	18	23	-	-	PUNCT
ejpam-1480	18	24	modules	module	NOUN
ejpam-1480	18	25	to	to	ADP
ejpam-1480	18	26	itself	itself	PRON
ejpam-1480	18	27	.	.	PUNCT
ejpam-1480	19	1	for	for	ADP
ejpam-1480	19	2	an	an	DET
ejpam-1480	19	3	integer	integer	NOUN
ejpam-1480	19	4	i	i	PRON
ejpam-1480	19	5	,	,	PUNCT
ejpam-1480	19	6	the	the	DET
ejpam-1480	19	7	local	local	ADJ
ejpam-1480	19	8	cohomology	cohomology	NOUN
ejpam-1480	19	9	functor	functor	PROPN
ejpam-1480	19	10	h	h	NOUN
ejpam-1480	20	1	i	i	PRON
ejpam-1480	20	2	i	i	PRON
ejpam-1480	20	3	,	,	PUNCT
ejpam-1480	20	4	j	j	PROPN
ejpam-1480	20	5	with	with	ADP
ejpam-1480	20	6	respect	respect	NOUN
ejpam-1480	20	7	to	to	ADP
ejpam-1480	20	8	(	(	PUNCT
ejpam-1480	20	9	i	i	PRON
ejpam-1480	20	10	,	,	PUNCT
ejpam-1480	20	11	j	j	PROPN
ejpam-1480	20	12	)	)	PUNCT
ejpam-1480	20	13	,	,	PUNCT
ejpam-1480	20	14	is	be	AUX
ejpam-1480	20	15	defined	define	VERB
ejpam-1480	20	16	to	to	PART
ejpam-1480	20	17	be	be	AUX
ejpam-1480	20	18	the	the	DET
ejpam-1480	20	19	i	i	PROPN
ejpam-1480	20	20	-	-	PUNCT
ejpam-1480	20	21	th	th	VERB
ejpam-1480	20	22	right	right	NOUN
ejpam-1480	20	23	derived	derive	VERB
ejpam-1480	20	24	functor	functor	NOUN
ejpam-1480	20	25	of	of	ADP
ejpam-1480	20	26	γi	γi	PROPN
ejpam-1480	20	27	,	,	PUNCT
ejpam-1480	20	28	j	j	PROPN
ejpam-1480	20	29	.	.	PUNCT
ejpam-1480	21	1	also	also	ADV
ejpam-1480	21	2	h	h	VERB
ejpam-1480	22	1	i	i	PRON
ejpam-1480	22	2	i	i	PRON
ejpam-1480	22	3	,	,	PUNCT
ejpam-1480	22	4	j(m	j(m	PROPN
ejpam-1480	22	5	)	)	PUNCT
ejpam-1480	22	6	is	be	AUX
ejpam-1480	22	7	called	call	VERB
ejpam-1480	22	8	∗corresponding	∗corresponde	VERB
ejpam-1480	22	9	author	author	NOUN
ejpam-1480	22	10	.	.	PUNCT
ejpam-1480	23	1	email	email	NOUN
ejpam-1480	23	2	addresses	address	NOUN
ejpam-1480	23	3	:	:	PUNCT
ejpam-1480	23	4	lotfi.parsa	lotfi.parsa	NOUN
ejpam-1480	23	5	�	�	PROPN
ejpam-1480	23	6	ikiu.a	ikiu.a	PROPN
ejpam-1480	23	7	.ir	.ir	PUNCT
ejpam-1480	24	1	(	(	PUNCT
ejpam-1480	24	2	m.	m.	NOUN
ejpam-1480	24	3	parsa	parsa	PROPN
ejpam-1480	24	4	)	)	PUNCT
ejpam-1480	24	5	,	,	PUNCT
ejpam-1480	24	6	shpayrovi	shpayrovi	PROPN
ejpam-1480	24	7	�	�	PROPN
ejpam-1480	24	8	ikiu.a	ikiu.a	PROPN
ejpam-1480	24	9	.ir	.ir	PUNCT
ejpam-1480	25	1	(	(	PUNCT
ejpam-1480	25	2	sh	sh	PROPN
ejpam-1480	25	3	.	.	PUNCT
ejpam-1480	25	4	payrovi	payrovi	PROPN
ejpam-1480	25	5	)	)	PUNCT
ejpam-1480	26	1	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1480	27	1	55	55	NUM
ejpam-1480	27	2	c	c	NOUN
ejpam-1480	27	3	©	©	PROPN
ejpam-1480	27	4	2012	2012	NUM
ejpam-1480	27	5	ejpam	ejpam	VERB
ejpam-1480	27	6	all	all	DET
ejpam-1480	27	7	rights	right	NOUN
ejpam-1480	27	8	reserved	reserve	VERB
ejpam-1480	27	9	.	.	PUNCT
ejpam-1480	28	1	m.	m.	NOUN
ejpam-1480	28	2	parsa	parsa	PROPN
ejpam-1480	28	3	,	,	PUNCT
ejpam-1480	28	4	sh	sh	PROPN
ejpam-1480	28	5	.	.	PROPN
ejpam-1480	28	6	payrovi	payrovi	PROPN
ejpam-1480	28	7	/	/	SYM
ejpam-1480	28	8	eur	eur	PROPN
ejpam-1480	28	9	.	.	PUNCT
ejpam-1480	29	1	j.	j.	PROPN
ejpam-1480	29	2	pure	pure	PROPN
ejpam-1480	29	3	appl	appl	PROPN
ejpam-1480	29	4	.	.	PROPN
ejpam-1480	29	5	math	math	PROPN
ejpam-1480	29	6	,	,	PUNCT
ejpam-1480	29	7	5	5	NUM
ejpam-1480	29	8	(	(	PUNCT
ejpam-1480	29	9	2012	2012	NUM
ejpam-1480	29	10	)	)	PUNCT
ejpam-1480	29	11	,	,	PUNCT
ejpam-1480	29	12	55	55	NUM
ejpam-1480	29	13	-	-	SYM
ejpam-1480	29	14	58	58	NUM
ejpam-1480	29	15	56	56	NUM
ejpam-1480	29	16	the	the	DET
ejpam-1480	29	17	i	i	PROPN
ejpam-1480	29	18	-	-	PUNCT
ejpam-1480	29	19	th	th	X
ejpam-1480	29	20	local	local	ADJ
ejpam-1480	29	21	cohomology	cohomology	NOUN
ejpam-1480	29	22	module	module	NOUN
ejpam-1480	29	23	of	of	ADP
ejpam-1480	29	24	m	m	PROPN
ejpam-1480	29	25	with	with	ADP
ejpam-1480	29	26	respect	respect	NOUN
ejpam-1480	29	27	to	to	ADP
ejpam-1480	29	28	(	(	PUNCT
ejpam-1480	29	29	i	i	PRON
ejpam-1480	29	30	,	,	PUNCT
ejpam-1480	29	31	j	j	PROPN
ejpam-1480	29	32	)	)	PUNCT
ejpam-1480	29	33	.	.	PUNCT
ejpam-1480	30	1	if	if	SCONJ
ejpam-1480	30	2	j	j	PROPN
ejpam-1480	30	3	=	=	SYM
ejpam-1480	30	4	0	0	PROPN
ejpam-1480	30	5	,	,	PUNCT
ejpam-1480	30	6	then	then	ADV
ejpam-1480	30	7	h	h	NOUN
ejpam-1480	31	1	i	i	PRON
ejpam-1480	31	2	i	i	PRON
ejpam-1480	31	3	,	,	PUNCT
ejpam-1480	31	4	j	j	PROPN
ejpam-1480	31	5	coincides	coincide	VERB
ejpam-1480	31	6	with	with	ADP
ejpam-1480	31	7	the	the	DET
ejpam-1480	31	8	ordinary	ordinary	ADJ
ejpam-1480	31	9	local	local	ADJ
ejpam-1480	31	10	cohomology	cohomology	NOUN
ejpam-1480	31	11	functor	functor	PROPN
ejpam-1480	31	12	h	h	NOUN
ejpam-1480	32	1	i	i	PRON
ejpam-1480	32	2	i	i	INTJ
ejpam-1480	32	3	.	.	PUNCT
ejpam-1480	33	1	some	some	DET
ejpam-1480	33	2	authors	author	NOUN
ejpam-1480	33	3	studied	study	VERB
ejpam-1480	33	4	the	the	DET
ejpam-1480	33	5	properties	property	NOUN
ejpam-1480	33	6	of	of	ADP
ejpam-1480	33	7	these	these	DET
ejpam-1480	33	8	extended	extended	ADJ
ejpam-1480	33	9	modules	module	NOUN
ejpam-1480	33	10	;	;	PUNCT
ejpam-1480	33	11	see	see	VERB
ejpam-1480	33	12	,	,	PUNCT
ejpam-1480	33	13	for	for	ADP
ejpam-1480	33	14	example	example	NOUN
ejpam-1480	33	15	,	,	PUNCT
ejpam-1480	33	16	[	[	X
ejpam-1480	33	17	2	2	NUM
ejpam-1480	33	18	,	,	PUNCT
ejpam-1480	33	19	3	3	NUM
ejpam-1480	33	20	,	,	PUNCT
ejpam-1480	33	21	5	5	NUM
ejpam-1480	33	22	,	,	PUNCT
ejpam-1480	33	23	7	7	NUM
ejpam-1480	33	24	]	]	PUNCT
ejpam-1480	33	25	.	.	PUNCT
ejpam-1480	34	1	in	in	ADP
ejpam-1480	34	2	this	this	DET
ejpam-1480	34	3	direction	direction	NOUN
ejpam-1480	34	4	,	,	PUNCT
ejpam-1480	34	5	we	we	PRON
ejpam-1480	34	6	study	study	VERB
ejpam-1480	34	7	artinianness	artinianness	ADJ
ejpam-1480	34	8	,	,	PUNCT
ejpam-1480	34	9	vanishing	vanishing	NOUN
ejpam-1480	34	10	and	and	CCONJ
ejpam-1480	34	11	finiteness	finiteness	NOUN
ejpam-1480	34	12	of	of	ADP
ejpam-1480	34	13	the	the	DET
ejpam-1480	34	14	local	local	ADJ
ejpam-1480	34	15	cohomology	cohomology	NOUN
ejpam-1480	34	16	modules	module	NOUN
ejpam-1480	34	17	defined	define	VERB
ejpam-1480	34	18	by	by	ADP
ejpam-1480	34	19	a	a	DET
ejpam-1480	34	20	pair	pair	NOUN
ejpam-1480	34	21	of	of	ADP
ejpam-1480	34	22	ideals	ideal	NOUN
ejpam-1480	34	23	.	.	PUNCT
ejpam-1480	35	1	suppose	suppose	VERB
ejpam-1480	35	2	that	that	SCONJ
ejpam-1480	35	3	m	m	PROPN
ejpam-1480	35	4	is	be	AUX
ejpam-1480	35	5	finitely	finitely	ADV
ejpam-1480	35	6	generated	generate	VERB
ejpam-1480	35	7	with	with	ADP
ejpam-1480	35	8	dimr	dimr	NOUN
ejpam-1480	35	9	m	m	PROPN
ejpam-1480	36	1	=	=	PUNCT
ejpam-1480	37	1	n.	n.	NOUN
ejpam-1480	38	1	it	it	PRON
ejpam-1480	38	2	is	be	AUX
ejpam-1480	38	3	well	well	ADV
ejpam-1480	38	4	known	know	VERB
ejpam-1480	38	5	that	that	SCONJ
ejpam-1480	38	6	hn	hn	PRON
ejpam-1480	38	7	i	i	PRON
ejpam-1480	38	8	(	(	PUNCT
ejpam-1480	38	9	m	m	NOUN
ejpam-1480	38	10	)	)	PUNCT
ejpam-1480	38	11	is	be	AUX
ejpam-1480	38	12	i	i	PROPN
ejpam-1480	38	13	-	-	PUNCT
ejpam-1480	38	14	cofinite	cofinite	NOUN
ejpam-1480	38	15	artinian	artinian	NOUN
ejpam-1480	38	16	;	;	PUNCT
ejpam-1480	38	17	[	[	X
ejpam-1480	38	18	see	see	VERB
ejpam-1480	38	19	4	4	NUM
ejpam-1480	38	20	,	,	PUNCT
ejpam-1480	38	21	proposition	proposition	NOUN
ejpam-1480	38	22	5.1	5.1	NUM
ejpam-1480	38	23	]	]	PUNCT
ejpam-1480	38	24	.	.	PUNCT
ejpam-1480	39	1	we	we	PRON
ejpam-1480	39	2	generalize	generalize	VERB
ejpam-1480	39	3	this	this	DET
ejpam-1480	39	4	result	result	NOUN
ejpam-1480	39	5	and	and	CCONJ
ejpam-1480	39	6	prove	prove	VERB
ejpam-1480	39	7	that	that	SCONJ
ejpam-1480	40	1	hn	hn	PROPN
ejpam-1480	40	2	i	i	PROPN
ejpam-1480	40	3	,	,	PUNCT
ejpam-1480	40	4	j(m)/jhn	j(m)/jhn	PROPN
ejpam-1480	41	1	i	i	PRON
ejpam-1480	41	2	,	,	PUNCT
ejpam-1480	41	3	j(m	j(m	PROPN
ejpam-1480	41	4	)	)	PUNCT
ejpam-1480	41	5	is	be	AUX
ejpam-1480	41	6	i	i	NOUN
ejpam-1480	41	7	-	-	PUNCT
ejpam-1480	41	8	cofinite	cofinite	NOUN
ejpam-1480	41	9	artinian	artinian	NOUN
ejpam-1480	41	10	.	.	PUNCT
ejpam-1480	42	1	let	let	VERB
ejpam-1480	42	2	r	r	NOUN
ejpam-1480	42	3	be	be	AUX
ejpam-1480	42	4	local	local	ADJ
ejpam-1480	42	5	and	and	CCONJ
ejpam-1480	42	6	m	m	AUX
ejpam-1480	42	7	finitely	finitely	ADV
ejpam-1480	42	8	generated	generate	VERB
ejpam-1480	42	9	with	with	ADP
ejpam-1480	42	10	dimr	dimr	NOUN
ejpam-1480	42	11	m	m	NOUN
ejpam-1480	42	12	=	=	SYM
ejpam-1480	42	13	n	n	CCONJ
ejpam-1480	42	14	>	>	X
ejpam-1480	42	15	0	0	NUM
ejpam-1480	42	16	.	.	PUNCT
ejpam-1480	43	1	it	it	PRON
ejpam-1480	43	2	follows	follow	VERB
ejpam-1480	43	3	by	by	ADP
ejpam-1480	43	4	grothendieck	grothendieck	PROPN
ejpam-1480	43	5	’s	’s	PART
ejpam-1480	43	6	non	non	ADJ
ejpam-1480	43	7	-	-	ADJ
ejpam-1480	43	8	vanishing	vanishing	ADJ
ejpam-1480	43	9	theorem	theorem	NOUN
ejpam-1480	43	10	that	that	PRON
ejpam-1480	43	11	hn	hn	PROPN
ejpam-1480	43	12	i	i	PRON
ejpam-1480	43	13	(	(	PUNCT
ejpam-1480	43	14	m	m	NOUN
ejpam-1480	43	15	)	)	PUNCT
ejpam-1480	43	16	is	be	AUX
ejpam-1480	43	17	not	not	PART
ejpam-1480	43	18	finitely	finitely	ADV
ejpam-1480	43	19	generated	generate	VERB
ejpam-1480	43	20	,	,	PUNCT
ejpam-1480	43	21	whenever	whenever	SCONJ
ejpam-1480	43	22	dim	dim	VERB
ejpam-1480	43	23	r	r	NOUN
ejpam-1480	43	24	/	/	SYM
ejpam-1480	43	25	i	i	NOUN
ejpam-1480	43	26	=	=	NOUN
ejpam-1480	43	27	0	0	X
ejpam-1480	43	28	.	.	PUNCT
ejpam-1480	44	1	as	as	ADP
ejpam-1480	44	2	a	a	DET
ejpam-1480	44	3	generalization	generalization	NOUN
ejpam-1480	44	4	of	of	ADP
ejpam-1480	44	5	this	this	DET
ejpam-1480	44	6	result	result	NOUN
ejpam-1480	44	7	,	,	PUNCT
ejpam-1480	44	8	we	we	PRON
ejpam-1480	44	9	show	show	VERB
ejpam-1480	44	10	that	that	SCONJ
ejpam-1480	44	11	if	if	SCONJ
ejpam-1480	44	12	dim	dim	ADJ
ejpam-1480	44	13	r	r	NOUN
ejpam-1480	44	14	/	/	SYM
ejpam-1480	44	15	i	i	PROPN
ejpam-1480	44	16	+	+	NUM
ejpam-1480	44	17	j	j	PROPN
ejpam-1480	44	18	=	=	SYM
ejpam-1480	44	19	0	0	NUM
ejpam-1480	44	20	and	and	CCONJ
ejpam-1480	44	21	dimr	dimr	NOUN
ejpam-1480	44	22	m	m	PROPN
ejpam-1480	44	23	/	/	SYM
ejpam-1480	44	24	j	j	PROPN
ejpam-1480	44	25	m	m	NOUN
ejpam-1480	44	26	=	=	SYM
ejpam-1480	45	1	d	d	X
ejpam-1480	45	2	>	>	X
ejpam-1480	45	3	0	0	PROPN
ejpam-1480	45	4	,	,	PUNCT
ejpam-1480	45	5	then	then	ADV
ejpam-1480	45	6	hd	hd	VERB
ejpam-1480	45	7	i	i	PRON
ejpam-1480	45	8	,	,	PUNCT
ejpam-1480	45	9	j(m	j(m	PROPN
ejpam-1480	45	10	)	)	PUNCT
ejpam-1480	45	11	is	be	AUX
ejpam-1480	45	12	not	not	PART
ejpam-1480	45	13	finitely	finitely	ADV
ejpam-1480	45	14	generated	generate	VERB
ejpam-1480	45	15	.	.	PUNCT
ejpam-1480	46	1	2	2	X
ejpam-1480	46	2	.	.	X
ejpam-1480	46	3	main	main	ADJ
ejpam-1480	46	4	results	result	NOUN
ejpam-1480	46	5	recall	recall	VERB
ejpam-1480	46	6	that	that	SCONJ
ejpam-1480	46	7	r	r	NOUN
ejpam-1480	46	8	is	be	AUX
ejpam-1480	46	9	a	a	DET
ejpam-1480	46	10	noetherian	noetherian	ADJ
ejpam-1480	46	11	ring	ring	NOUN
ejpam-1480	46	12	,	,	PUNCT
ejpam-1480	46	13	i	i	PRON
ejpam-1480	46	14	,	,	PUNCT
ejpam-1480	46	15	j	j	PROPN
ejpam-1480	46	16	are	be	AUX
ejpam-1480	46	17	two	two	NUM
ejpam-1480	46	18	ideals	ideal	NOUN
ejpam-1480	46	19	of	of	ADP
ejpam-1480	46	20	r	r	NOUN
ejpam-1480	46	21	and	and	CCONJ
ejpam-1480	46	22	m	m	PROPN
ejpam-1480	46	23	is	be	AUX
ejpam-1480	46	24	an	an	DET
ejpam-1480	46	25	r	r	NOUN
ejpam-1480	46	26	-	-	PUNCT
ejpam-1480	46	27	module	module	NOUN
ejpam-1480	46	28	.	.	PUNCT
ejpam-1480	47	1	the	the	DET
ejpam-1480	47	2	following	following	ADJ
ejpam-1480	47	3	result	result	NOUN
ejpam-1480	47	4	improves	improve	VERB
ejpam-1480	47	5	[	[	X
ejpam-1480	47	6	5	5	NUM
ejpam-1480	47	7	,	,	PUNCT
ejpam-1480	47	8	corollary	corollary	ADJ
ejpam-1480	47	9	3.5	3.5	NUM
ejpam-1480	47	10	]	]	PUNCT
ejpam-1480	47	11	.	.	PUNCT
ejpam-1480	48	1	theorem	theorem	NOUN
ejpam-1480	48	2	1	1	X
ejpam-1480	48	3	.	.	PUNCT
ejpam-1480	49	1	let	let	VERB
ejpam-1480	49	2	m	m	PRON
ejpam-1480	49	3	be	be	AUX
ejpam-1480	49	4	finitely	finitely	ADV
ejpam-1480	49	5	generated	generate	VERB
ejpam-1480	49	6	with	with	ADP
ejpam-1480	49	7	dimr	dimr	NOUN
ejpam-1480	49	8	m	m	NOUN
ejpam-1480	50	1	=	=	VERB
ejpam-1480	50	2	n.	n.	NOUN
ejpam-1480	51	1	then	then	ADV
ejpam-1480	51	2	hn	hn	PROPN
ejpam-1480	51	3	i	i	PROPN
ejpam-1480	51	4	,	,	PUNCT
ejpam-1480	51	5	j(m)/jhn	j(m)/jhn	PROPN
ejpam-1480	52	1	i	i	PRON
ejpam-1480	52	2	,	,	PUNCT
ejpam-1480	52	3	j(m	j(m	PROPN
ejpam-1480	52	4	)	)	PUNCT
ejpam-1480	52	5	is	be	AUX
ejpam-1480	52	6	i	i	NOUN
ejpam-1480	52	7	-	-	PUNCT
ejpam-1480	52	8	cofinite	cofinite	NOUN
ejpam-1480	52	9	artinian	artinian	NOUN
ejpam-1480	52	10	.	.	PUNCT
ejpam-1480	53	1	proof	proof	NOUN
ejpam-1480	53	2	.	.	PUNCT
ejpam-1480	54	1	we	we	PRON
ejpam-1480	54	2	use	use	VERB
ejpam-1480	54	3	induction	induction	NOUN
ejpam-1480	54	4	on	on	ADP
ejpam-1480	54	5	n.	n.	PROPN
ejpam-1480	54	6	if	if	SCONJ
ejpam-1480	54	7	n=	n=	ADJ
ejpam-1480	54	8	0	0	NUM
ejpam-1480	54	9	,	,	PUNCT
ejpam-1480	54	10	then	then	ADV
ejpam-1480	54	11	m	m	PROPN
ejpam-1480	54	12	has	have	VERB
ejpam-1480	54	13	finite	finite	ADJ
ejpam-1480	54	14	length	length	NOUN
ejpam-1480	54	15	.	.	PUNCT
ejpam-1480	55	1	therefore	therefore	ADV
ejpam-1480	55	2	γi	γi	INTJ
ejpam-1480	55	3	,	,	PUNCT
ejpam-1480	55	4	j(m)/jγi	j(m)/jγi	X
ejpam-1480	55	5	,	,	PUNCT
ejpam-1480	55	6	j(m	j(m	PROPN
ejpam-1480	55	7	)	)	PUNCT
ejpam-1480	55	8	has	have	VERB
ejpam-1480	55	9	finite	finite	ADJ
ejpam-1480	55	10	length	length	NOUN
ejpam-1480	55	11	and	and	CCONJ
ejpam-1480	55	12	so	so	ADV
ejpam-1480	55	13	γi	γi	INTJ
ejpam-1480	55	14	,	,	PUNCT
ejpam-1480	55	15	j(m)/jγi	j(m)/jγi	X
ejpam-1480	55	16	,	,	PUNCT
ejpam-1480	55	17	j(m	j(m	PROPN
ejpam-1480	55	18	)	)	PUNCT
ejpam-1480	55	19	is	be	AUX
ejpam-1480	55	20	i	i	NOUN
ejpam-1480	55	21	-	-	PUNCT
ejpam-1480	55	22	cofinite	cofinite	NOUN
ejpam-1480	55	23	artinian	artinian	NOUN
ejpam-1480	55	24	.	.	PUNCT
ejpam-1480	56	1	now	now	ADV
ejpam-1480	56	2	suppose	suppose	VERB
ejpam-1480	56	3	,	,	PUNCT
ejpam-1480	56	4	inductively	inductively	ADV
ejpam-1480	56	5	,	,	PUNCT
ejpam-1480	56	6	that	that	SCONJ
ejpam-1480	56	7	n	n	CCONJ
ejpam-1480	56	8	>	>	X
ejpam-1480	56	9	0	0	NUM
ejpam-1480	56	10	,	,	PUNCT
ejpam-1480	56	11	and	and	CCONJ
ejpam-1480	56	12	the	the	DET
ejpam-1480	56	13	result	result	NOUN
ejpam-1480	56	14	has	have	AUX
ejpam-1480	56	15	been	be	AUX
ejpam-1480	56	16	proved	prove	VERB
ejpam-1480	56	17	for	for	ADP
ejpam-1480	56	18	all	all	DET
ejpam-1480	56	19	r	r	NOUN
ejpam-1480	56	20	-	-	PUNCT
ejpam-1480	56	21	modules	module	NOUN
ejpam-1480	56	22	of	of	ADP
ejpam-1480	56	23	dimensions	dimension	NOUN
ejpam-1480	56	24	smaller	small	ADJ
ejpam-1480	56	25	than	than	ADP
ejpam-1480	56	26	n	n	PRON
ejpam-1480	56	27	satisfying	satisfy	VERB
ejpam-1480	56	28	the	the	DET
ejpam-1480	56	29	hypothesis	hypothesis	NOUN
ejpam-1480	56	30	.	.	PUNCT
ejpam-1480	57	1	since	since	SCONJ
ejpam-1480	57	2	hn	hn	PROPN
ejpam-1480	57	3	i	i	PROPN
ejpam-1480	57	4	,	,	PUNCT
ejpam-1480	57	5	j(m	j(m	PROPN
ejpam-1480	57	6	/	/	SYM
ejpam-1480	57	7	γi	γi	PROPN
ejpam-1480	57	8	,	,	PUNCT
ejpam-1480	57	9	j(m	j(m	PROPN
ejpam-1480	57	10	)	)	PUNCT
ejpam-1480	57	11	)	)	PUNCT
ejpam-1480	57	12	∼=	∼=	PROPN
ejpam-1480	57	13	hn	hn	PROPN
ejpam-1480	57	14	i	i	PROPN
ejpam-1480	57	15	,	,	PUNCT
ejpam-1480	57	16	j(m	j(m	PROPN
ejpam-1480	57	17	)	)	PUNCT
ejpam-1480	57	18	by	by	ADP
ejpam-1480	57	19	[	[	X
ejpam-1480	57	20	6	6	NUM
ejpam-1480	57	21	,	,	PUNCT
ejpam-1480	57	22	corollary	corollary	ADJ
ejpam-1480	57	23	1.13(4	1.13(4	NUM
ejpam-1480	57	24	)	)	PUNCT
ejpam-1480	57	25	]	]	PUNCT
ejpam-1480	57	26	,	,	PUNCT
ejpam-1480	57	27	we	we	PRON
ejpam-1480	57	28	may	may	AUX
ejpam-1480	57	29	assume	assume	VERB
ejpam-1480	57	30	in	in	ADP
ejpam-1480	57	31	addition	addition	NOUN
ejpam-1480	57	32	that	that	SCONJ
ejpam-1480	57	33	m	m	NOUN
ejpam-1480	57	34	is	be	AUX
ejpam-1480	57	35	an	an	DET
ejpam-1480	57	36	(	(	PUNCT
ejpam-1480	57	37	i	i	NOUN
ejpam-1480	57	38	,	,	PUNCT
ejpam-1480	57	39	j)-torsion	j)-torsion	NOUN
ejpam-1480	57	40	free	free	ADJ
ejpam-1480	57	41	r	r	NOUN
ejpam-1480	57	42	-	-	PUNCT
ejpam-1480	57	43	module	module	NOUN
ejpam-1480	57	44	.	.	PUNCT
ejpam-1480	58	1	thus	thus	ADV
ejpam-1480	58	2	i	i	PRON
ejpam-1480	58	3	contains	contain	VERB
ejpam-1480	58	4	an	an	DET
ejpam-1480	58	5	element	element	NOUN
ejpam-1480	58	6	a	a	DET
ejpam-1480	58	7	which	which	PRON
ejpam-1480	58	8	is	be	AUX
ejpam-1480	58	9	non	non	ADJ
ejpam-1480	58	10	zero	zero	NUM
ejpam-1480	58	11	-	-	PUNCT
ejpam-1480	58	12	divisor	divisor	NOUN
ejpam-1480	58	13	on	on	ADP
ejpam-1480	58	14	m	m	PROPN
ejpam-1480	58	15	.	.	PUNCT
ejpam-1480	59	1	since	since	SCONJ
ejpam-1480	59	2	dim	dim	ADJ
ejpam-1480	59	3	m	m	PROPN
ejpam-1480	59	4	/	/	SYM
ejpam-1480	59	5	am	be	AUX
ejpam-1480	59	6	≤	≤	NUM
ejpam-1480	59	7	n−	n−	NOUN
ejpam-1480	59	8	1	1	NUM
ejpam-1480	59	9	,	,	PUNCT
ejpam-1480	59	10	it	it	PRON
ejpam-1480	59	11	follows	follow	VERB
ejpam-1480	59	12	by	by	ADP
ejpam-1480	59	13	the	the	DET
ejpam-1480	59	14	inductive	inductive	ADJ
ejpam-1480	59	15	hypothesis	hypothesis	NOUN
ejpam-1480	59	16	that	that	PRON
ejpam-1480	59	17	hn−1	hn−1	PROPN
ejpam-1480	59	18	i	i	PROPN
ejpam-1480	59	19	,	,	PUNCT
ejpam-1480	59	20	j	j	PROPN
ejpam-1480	59	21	(	(	PUNCT
ejpam-1480	59	22	m	m	PROPN
ejpam-1480	59	23	/	/	SYM
ejpam-1480	59	24	am)/jhn−1	am)/jhn−1	PROPN
ejpam-1480	60	1	i	i	PRON
ejpam-1480	60	2	,	,	PUNCT
ejpam-1480	60	3	j	j	PROPN
ejpam-1480	60	4	(	(	PUNCT
ejpam-1480	60	5	m	m	PROPN
ejpam-1480	60	6	/	/	SYM
ejpam-1480	60	7	am	be	AUX
ejpam-1480	60	8	)	)	PUNCT
ejpam-1480	60	9	is	be	AUX
ejpam-1480	60	10	i	i	NOUN
ejpam-1480	60	11	-	-	PUNCT
ejpam-1480	60	12	cofinite	cofinite	NOUN
ejpam-1480	60	13	artinian	artinian	NOUN
ejpam-1480	60	14	.	.	PUNCT
ejpam-1480	61	1	the	the	DET
ejpam-1480	61	2	exact	exact	ADJ
ejpam-1480	61	3	sequence	sequence	NOUN
ejpam-1480	61	4	0→	0→	PROPN
ejpam-1480	61	5	m	m	VERB
ejpam-1480	61	6	a	a	DET
ejpam-1480	61	7	→	→	NOUN
ejpam-1480	61	8	m	m	PROPN
ejpam-1480	61	9	→	→	SYM
ejpam-1480	61	10	m	m	NOUN
ejpam-1480	61	11	/	/	SYM
ejpam-1480	61	12	am	be	AUX
ejpam-1480	61	13	→	→	SYM
ejpam-1480	61	14	0	0	NUM
ejpam-1480	61	15	induces	induce	VERB
ejpam-1480	61	16	an	an	DET
ejpam-1480	61	17	exact	exact	ADJ
ejpam-1480	61	18	sequence	sequence	NOUN
ejpam-1480	61	19	·	·	PUNCT
ejpam-1480	61	20	·	·	PUNCT
ejpam-1480	61	21	·	·	PUNCT
ejpam-1480	62	1	→	→	PUNCT
ejpam-1480	62	2	hn−1	hn−1	PROPN
ejpam-1480	62	3	i	i	PROPN
ejpam-1480	62	4	,	,	PUNCT
ejpam-1480	62	5	j	j	PROPN
ejpam-1480	62	6	(	(	PUNCT
ejpam-1480	62	7	m	m	NOUN
ejpam-1480	62	8	/	/	SYM
ejpam-1480	62	9	am)→	am)→	ADJ
ejpam-1480	62	10	hn	hn	PROPN
ejpam-1480	62	11	i	i	PROPN
ejpam-1480	62	12	,	,	PUNCT
ejpam-1480	62	13	j(m	j(m	PROPN
ejpam-1480	62	14	)	)	PUNCT
ejpam-1480	62	15	a	a	DET
ejpam-1480	62	16	→	→	X
ejpam-1480	62	17	hn	hn	PROPN
ejpam-1480	62	18	i	i	PRON
ejpam-1480	62	19	,	,	PUNCT
ejpam-1480	62	20	j(m)→	j(m)→	NOUN
ejpam-1480	62	21	0	0	NUM
ejpam-1480	62	22	of	of	ADP
ejpam-1480	62	23	local	local	ADJ
ejpam-1480	62	24	cohomology	cohomology	NOUN
ejpam-1480	62	25	modules	module	NOUN
ejpam-1480	62	26	.	.	PUNCT
ejpam-1480	63	1	now	now	ADV
ejpam-1480	63	2	the	the	DET
ejpam-1480	63	3	exact	exact	ADJ
ejpam-1480	63	4	sequence	sequence	NOUN
ejpam-1480	63	5	hn−1	hn−1	PROPN
ejpam-1480	63	6	i	i	PROPN
ejpam-1480	63	7	,	,	PUNCT
ejpam-1480	63	8	j	j	PROPN
ejpam-1480	63	9	(	(	PUNCT
ejpam-1480	63	10	m	m	PROPN
ejpam-1480	63	11	/	/	SYM
ejpam-1480	64	1	am)/jhn−1	am)/jhn−1	PROPN
ejpam-1480	64	2	i	i	PRON
ejpam-1480	64	3	,	,	PUNCT
ejpam-1480	64	4	j	j	PROPN
ejpam-1480	64	5	(	(	PUNCT
ejpam-1480	64	6	m	m	NOUN
ejpam-1480	64	7	/	/	SYM
ejpam-1480	64	8	am)→	am)→	ADJ
ejpam-1480	64	9	hn	hn	PROPN
ejpam-1480	64	10	i	i	PROPN
ejpam-1480	64	11	,	,	PUNCT
ejpam-1480	64	12	j(m)/jhn	j(m)/jhn	PROPN
ejpam-1480	65	1	i	i	PRON
ejpam-1480	65	2	,	,	PUNCT
ejpam-1480	65	3	j(m	j(m	PROPN
ejpam-1480	65	4	)	)	PUNCT
ejpam-1480	65	5	a	a	DET
ejpam-1480	65	6	→	→	X
ejpam-1480	65	7	hn	hn	PROPN
ejpam-1480	65	8	i	i	PROPN
ejpam-1480	65	9	,	,	PUNCT
ejpam-1480	65	10	j(m)/jhn	j(m)/jhn	PROPN
ejpam-1480	66	1	i	i	PRON
ejpam-1480	66	2	,	,	PUNCT
ejpam-1480	66	3	j(m)→	j(m)→	NOUN
ejpam-1480	66	4	0	0	NUM
ejpam-1480	66	5	implies	imply	VERB
ejpam-1480	66	6	that	that	SCONJ
ejpam-1480	66	7	0	0	X
ejpam-1480	66	8	:	:	PUNCT
ejpam-1480	66	9	hn	hn	PROPN
ejpam-1480	67	1	i	i	PROPN
ejpam-1480	67	2	,	,	PUNCT
ejpam-1480	67	3	j	j	PROPN
ejpam-1480	67	4	(	(	PUNCT
ejpam-1480	67	5	m)/jhn	m)/jhn	INTJ
ejpam-1480	67	6	i	i	PROPN
ejpam-1480	67	7	,	,	PUNCT
ejpam-1480	67	8	j	j	PROPN
ejpam-1480	67	9	(	(	PUNCT
ejpam-1480	67	10	m	m	PROPN
ejpam-1480	67	11	)	)	PUNCT
ejpam-1480	68	1	a	a	PRON
ejpam-1480	68	2	is	be	AUX
ejpam-1480	68	3	i	i	NOUN
ejpam-1480	68	4	-	-	PUNCT
ejpam-1480	68	5	cofinite	cofinite	NOUN
ejpam-1480	68	6	artinian	artinian	NOUN
ejpam-1480	68	7	.	.	PUNCT
ejpam-1480	69	1	therefore	therefore	ADV
ejpam-1480	69	2	hn	hn	PROPN
ejpam-1480	69	3	i	i	PROPN
ejpam-1480	69	4	,	,	PUNCT
ejpam-1480	69	5	j(m)/jhn	j(m)/jhn	PROPN
ejpam-1480	69	6	i	i	PRON
ejpam-1480	69	7	,	,	PUNCT
ejpam-1480	69	8	j(m	j(m	PROPN
ejpam-1480	69	9	)	)	PUNCT
ejpam-1480	69	10	is	be	AUX
ejpam-1480	69	11	i	i	NOUN
ejpam-1480	69	12	-	-	PUNCT
ejpam-1480	69	13	cofinite	cofinite	NOUN
ejpam-1480	69	14	artinian	artinian	NOUN
ejpam-1480	69	15	,	,	PUNCT
ejpam-1480	69	16	by	by	ADP
ejpam-1480	69	17	[	[	X
ejpam-1480	69	18	4	4	NUM
ejpam-1480	69	19	,	,	PUNCT
ejpam-1480	69	20	proposition	proposition	NOUN
ejpam-1480	69	21	4.1	4.1	NUM
ejpam-1480	69	22	]	]	PUNCT
ejpam-1480	69	23	.	.	PUNCT
ejpam-1480	70	1	this	this	PRON
ejpam-1480	70	2	completes	complete	VERB
ejpam-1480	70	3	the	the	DET
ejpam-1480	70	4	inductive	inductive	ADJ
ejpam-1480	70	5	step	step	NOUN
ejpam-1480	70	6	.	.	PUNCT
ejpam-1480	71	1	the	the	DET
ejpam-1480	71	2	result	result	NOUN
ejpam-1480	71	3	follows	follow	VERB
ejpam-1480	71	4	by	by	ADP
ejpam-1480	71	5	induction	induction	NOUN
ejpam-1480	71	6	.	.	PUNCT
ejpam-1480	72	1	let	let	VERB
ejpam-1480	72	2	w̃(i	w̃(i	PROPN
ejpam-1480	72	3	,	,	PUNCT
ejpam-1480	72	4	j	j	PROPN
ejpam-1480	72	5	)	)	PUNCT
ejpam-1480	72	6	denote	denote	VERB
ejpam-1480	72	7	the	the	DET
ejpam-1480	72	8	set	set	NOUN
ejpam-1480	72	9	of	of	ADP
ejpam-1480	72	10	ideals	ideal	NOUN
ejpam-1480	72	11	a	a	PRON
ejpam-1480	72	12	of	of	ADP
ejpam-1480	72	13	r	r	NOUN
ejpam-1480	72	14	such	such	ADJ
ejpam-1480	72	15	that	that	SCONJ
ejpam-1480	72	16	i	i	PRON
ejpam-1480	72	17	t	t	VERB
ejpam-1480	72	18	⊆	⊆	NUM
ejpam-1480	72	19	a+	a+	PUNCT
ejpam-1480	72	20	j	j	NOUN
ejpam-1480	72	21	for	for	ADP
ejpam-1480	72	22	some	some	DET
ejpam-1480	72	23	positive	positive	ADJ
ejpam-1480	72	24	integer	integer	NOUN
ejpam-1480	72	25	t.	t.	NOUN
ejpam-1480	73	1	it	it	PRON
ejpam-1480	73	2	is	be	AUX
ejpam-1480	73	3	easy	easy	ADJ
ejpam-1480	73	4	to	to	PART
ejpam-1480	73	5	see	see	VERB
ejpam-1480	73	6	that	that	PRON
ejpam-1480	73	7	,	,	PUNCT
ejpam-1480	73	8	for	for	ADP
ejpam-1480	73	9	any	any	DET
ejpam-1480	73	10	a	a	DET
ejpam-1480	73	11	∈	∈	PROPN
ejpam-1480	73	12	w̃(i	w̃(i	PROPN
ejpam-1480	73	13	,	,	PUNCT
ejpam-1480	73	14	j	j	PROPN
ejpam-1480	73	15	)	)	PUNCT
ejpam-1480	73	16	,	,	PUNCT
ejpam-1480	73	17	γa(m	γa(m	NUM
ejpam-1480	73	18	)	)	PUNCT
ejpam-1480	73	19	is	be	AUX
ejpam-1480	73	20	a	a	DET
ejpam-1480	73	21	subset	subset	NOUN
ejpam-1480	73	22	of	of	ADP
ejpam-1480	73	23	γi	γi	PROPN
ejpam-1480	73	24	,	,	PUNCT
ejpam-1480	73	25	j(m	j(m	PROPN
ejpam-1480	73	26	)	)	PUNCT
ejpam-1480	73	27	.	.	PUNCT
ejpam-1480	74	1	theorem	theorem	NOUN
ejpam-1480	74	2	2	2	NUM
ejpam-1480	74	3	.	.	PUNCT
ejpam-1480	75	1	let	let	VERB
ejpam-1480	75	2	m	m	PRON
ejpam-1480	75	3	be	be	AUX
ejpam-1480	75	4	finitely	finitely	ADV
ejpam-1480	75	5	generated	generate	VERB
ejpam-1480	75	6	with	with	ADP
ejpam-1480	75	7	dimr	dimr	NOUN
ejpam-1480	75	8	m	m	PROPN
ejpam-1480	75	9	=	=	SYM
ejpam-1480	76	1	n	n	PROPN
ejpam-1480	77	1	and	and	CCONJ
ejpam-1480	77	2	t	t	X
ejpam-1480	77	3	a	a	DET
ejpam-1480	77	4	positive	positive	ADJ
ejpam-1480	77	5	integer	integer	NOUN
ejpam-1480	77	6	.	.	PUNCT
ejpam-1480	78	1	if	if	SCONJ
ejpam-1480	78	2	h	h	PRON
ejpam-1480	78	3	i	i	PRON
ejpam-1480	78	4	i	i	PRON
ejpam-1480	78	5	,	,	PUNCT
ejpam-1480	78	6	j(m	j(m	PROPN
ejpam-1480	78	7	)	)	PUNCT
ejpam-1480	79	1	=	=	SYM
ejpam-1480	79	2	0	0	NUM
ejpam-1480	79	3	,	,	PUNCT
ejpam-1480	79	4	for	for	ADP
ejpam-1480	79	5	all	all	PRON
ejpam-1480	79	6	i	i	PRON
ejpam-1480	79	7	>	>	X
ejpam-1480	79	8	t	t	PROPN
ejpam-1480	80	1	,	,	PUNCT
ejpam-1480	80	2	then	then	ADV
ejpam-1480	80	3	h	h	PROPN
ejpam-1480	80	4	t	t	PROPN
ejpam-1480	80	5	i	i	PRON
ejpam-1480	80	6	,	,	PUNCT
ejpam-1480	80	7	j(m)/ah	j(m)/ah	PROPN
ejpam-1480	80	8	t	t	PROPN
ejpam-1480	80	9	i	i	PRON
ejpam-1480	80	10	,	,	PUNCT
ejpam-1480	80	11	j(m	j(m	PROPN
ejpam-1480	80	12	)	)	PUNCT
ejpam-1480	81	1	=	=	SYM
ejpam-1480	81	2	0	0	NUM
ejpam-1480	81	3	,	,	PUNCT
ejpam-1480	81	4	for	for	ADP
ejpam-1480	81	5	any	any	DET
ejpam-1480	81	6	a	a	DET
ejpam-1480	81	7	∈	∈	PROPN
ejpam-1480	81	8	w̃(i	w̃(i	PROPN
ejpam-1480	81	9	,	,	PUNCT
ejpam-1480	81	10	j	j	PROPN
ejpam-1480	81	11	)	)	PUNCT
ejpam-1480	81	12	.	.	PUNCT
ejpam-1480	82	1	m.	m.	PROPN
ejpam-1480	82	2	parsa	parsa	PROPN
ejpam-1480	82	3	,	,	PUNCT
ejpam-1480	82	4	sh	sh	PROPN
ejpam-1480	82	5	.	.	PROPN
ejpam-1480	82	6	payrovi	payrovi	PROPN
ejpam-1480	82	7	/	/	SYM
ejpam-1480	82	8	eur	eur	PROPN
ejpam-1480	82	9	.	.	PUNCT
ejpam-1480	83	1	j.	j.	PROPN
ejpam-1480	83	2	pure	pure	PROPN
ejpam-1480	83	3	appl	appl	PROPN
ejpam-1480	83	4	.	.	PROPN
ejpam-1480	83	5	math	math	PROPN
ejpam-1480	83	6	,	,	PUNCT
ejpam-1480	83	7	5	5	NUM
ejpam-1480	83	8	(	(	PUNCT
ejpam-1480	83	9	2012	2012	NUM
ejpam-1480	83	10	)	)	PUNCT
ejpam-1480	83	11	,	,	PUNCT
ejpam-1480	83	12	55	55	NUM
ejpam-1480	83	13	-	-	SYM
ejpam-1480	83	14	58	58	NUM
ejpam-1480	83	15	57	57	NUM
ejpam-1480	83	16	proof	proof	NOUN
ejpam-1480	83	17	.	.	PUNCT
ejpam-1480	84	1	let	let	VERB
ejpam-1480	84	2	a	a	DET
ejpam-1480	84	3	∈	∈	ADJ
ejpam-1480	84	4	w̃(i	w̃(i	PROPN
ejpam-1480	84	5	,	,	PUNCT
ejpam-1480	84	6	j	j	PROPN
ejpam-1480	84	7	)	)	PUNCT
ejpam-1480	84	8	be	be	AUX
ejpam-1480	84	9	fixed	fix	VERB
ejpam-1480	84	10	.	.	PUNCT
ejpam-1480	85	1	we	we	PRON
ejpam-1480	85	2	prove	prove	VERB
ejpam-1480	85	3	the	the	DET
ejpam-1480	85	4	claim	claim	NOUN
ejpam-1480	85	5	by	by	ADP
ejpam-1480	85	6	using	use	VERB
ejpam-1480	85	7	induction	induction	NOUN
ejpam-1480	85	8	on	on	ADP
ejpam-1480	85	9	n.	n.	PROPN
ejpam-1480	85	10	if	if	SCONJ
ejpam-1480	85	11	n=	n=	ADJ
ejpam-1480	85	12	0	0	NUM
ejpam-1480	85	13	,	,	PUNCT
ejpam-1480	85	14	then	then	ADV
ejpam-1480	85	15	the	the	DET
ejpam-1480	85	16	claim	claim	NOUN
ejpam-1480	85	17	is	be	AUX
ejpam-1480	85	18	clear	clear	ADJ
ejpam-1480	85	19	.	.	PUNCT
ejpam-1480	86	1	assume	assume	VERB
ejpam-1480	86	2	,	,	PUNCT
ejpam-1480	86	3	inductively	inductively	ADV
ejpam-1480	86	4	,	,	PUNCT
ejpam-1480	86	5	that	that	SCONJ
ejpam-1480	86	6	n	n	CCONJ
ejpam-1480	86	7	>	>	X
ejpam-1480	86	8	0	0	PUNCT
ejpam-1480	87	1	and	and	CCONJ
ejpam-1480	87	2	the	the	DET
ejpam-1480	87	3	result	result	NOUN
ejpam-1480	87	4	has	have	AUX
ejpam-1480	87	5	been	be	AUX
ejpam-1480	87	6	proved	prove	VERB
ejpam-1480	87	7	for	for	ADP
ejpam-1480	87	8	any	any	DET
ejpam-1480	87	9	rmodule	rmodule	NOUN
ejpam-1480	87	10	of	of	ADP
ejpam-1480	87	11	dimension	dimension	NOUN
ejpam-1480	87	12	less	less	ADJ
ejpam-1480	87	13	than	than	ADP
ejpam-1480	87	14	n	n	PRON
ejpam-1480	87	15	satisfying	satisfy	VERB
ejpam-1480	87	16	the	the	DET
ejpam-1480	87	17	hypothesis	hypothesis	NOUN
ejpam-1480	87	18	.	.	PUNCT
ejpam-1480	88	1	since	since	SCONJ
ejpam-1480	88	2	h	h	PROPN
ejpam-1480	88	3	i	i	PRON
ejpam-1480	88	4	i	i	PRON
ejpam-1480	88	5	,	,	PUNCT
ejpam-1480	88	6	j(m	j(m	PROPN
ejpam-1480	88	7	/	/	SYM
ejpam-1480	88	8	γi	γi	PROPN
ejpam-1480	88	9	,	,	PUNCT
ejpam-1480	88	10	j(m	j(m	PROPN
ejpam-1480	88	11	)	)	PUNCT
ejpam-1480	88	12	)	)	PUNCT
ejpam-1480	89	1	∼=	∼=	NOUN
ejpam-1480	89	2	h	h	NOUN
ejpam-1480	90	1	i	i	PRON
ejpam-1480	90	2	i	i	PRON
ejpam-1480	90	3	,	,	PUNCT
ejpam-1480	90	4	j(m	j(m	PROPN
ejpam-1480	90	5	)	)	PUNCT
ejpam-1480	90	6	for	for	ADP
ejpam-1480	90	7	all	all	DET
ejpam-1480	90	8	i	i	PRON
ejpam-1480	90	9	>	>	X
ejpam-1480	90	10	0	0	NUM
ejpam-1480	90	11	,	,	PUNCT
ejpam-1480	90	12	by	by	ADP
ejpam-1480	90	13	[	[	X
ejpam-1480	90	14	6	6	NUM
ejpam-1480	90	15	,	,	PUNCT
ejpam-1480	90	16	corollary	corollary	ADJ
ejpam-1480	90	17	1.13(4	1.13(4	NUM
ejpam-1480	90	18	)	)	PUNCT
ejpam-1480	90	19	]	]	PUNCT
ejpam-1480	90	20	,	,	PUNCT
ejpam-1480	90	21	we	we	PRON
ejpam-1480	90	22	may	may	AUX
ejpam-1480	90	23	assume	assume	VERB
ejpam-1480	90	24	in	in	ADP
ejpam-1480	90	25	addition	addition	NOUN
ejpam-1480	90	26	that	that	SCONJ
ejpam-1480	90	27	γi	γi	PROPN
ejpam-1480	90	28	,	,	PUNCT
ejpam-1480	90	29	j(m	j(m	PROPN
ejpam-1480	90	30	)	)	PUNCT
ejpam-1480	90	31	=	=	SYM
ejpam-1480	91	1	0	0	X
ejpam-1480	91	2	.	.	PUNCT
ejpam-1480	92	1	we	we	PRON
ejpam-1480	92	2	have	have	VERB
ejpam-1480	92	3	γa(m	γa(m	NOUN
ejpam-1480	92	4	)	)	PUNCT
ejpam-1480	92	5	⊆	⊆	NUM
ejpam-1480	92	6	γi	γi	NOUN
ejpam-1480	92	7	,	,	PUNCT
ejpam-1480	92	8	j(m	j(m	PROPN
ejpam-1480	92	9	)	)	PUNCT
ejpam-1480	92	10	,	,	PUNCT
ejpam-1480	92	11	thus	thus	ADV
ejpam-1480	92	12	γa(m	γa(m	PUNCT
ejpam-1480	92	13	)	)	PUNCT
ejpam-1480	92	14	=	=	SYM
ejpam-1480	92	15	0	0	NUM
ejpam-1480	92	16	,	,	PUNCT
ejpam-1480	92	17	and	and	CCONJ
ejpam-1480	92	18	therefore	therefore	ADV
ejpam-1480	92	19	a	a	PRON
ejpam-1480	92	20	contains	contain	VERB
ejpam-1480	92	21	an	an	DET
ejpam-1480	92	22	element	element	NOUN
ejpam-1480	92	23	a	a	DET
ejpam-1480	92	24	which	which	PRON
ejpam-1480	92	25	is	be	AUX
ejpam-1480	92	26	non	non	ADJ
ejpam-1480	92	27	zero	zero	NUM
ejpam-1480	92	28	-	-	PUNCT
ejpam-1480	92	29	divisor	divisor	NOUN
ejpam-1480	92	30	on	on	ADP
ejpam-1480	92	31	m	m	PROPN
ejpam-1480	92	32	.	.	PUNCT
ejpam-1480	93	1	the	the	DET
ejpam-1480	93	2	exact	exact	ADJ
ejpam-1480	93	3	sequence	sequence	NOUN
ejpam-1480	93	4	0	0	NUM
ejpam-1480	94	1	→	→	SYM
ejpam-1480	94	2	m	m	VERB
ejpam-1480	94	3	a	a	DET
ejpam-1480	94	4	→	→	NOUN
ejpam-1480	94	5	m	m	PROPN
ejpam-1480	94	6	→	→	SYM
ejpam-1480	94	7	m	m	NOUN
ejpam-1480	94	8	/	/	SYM
ejpam-1480	94	9	am	be	AUX
ejpam-1480	94	10	→	→	SYM
ejpam-1480	94	11	0	0	NUM
ejpam-1480	94	12	induces	induce	VERB
ejpam-1480	94	13	the	the	DET
ejpam-1480	94	14	following	follow	VERB
ejpam-1480	94	15	exact	exact	ADJ
ejpam-1480	94	16	sequence	sequence	NOUN
ejpam-1480	94	17	·	·	PUNCT
ejpam-1480	94	18	·	·	PUNCT
ejpam-1480	94	19	·	·	PUNCT
ejpam-1480	95	1	→	→	PUNCT
ejpam-1480	95	2	h	h	NOUN
ejpam-1480	96	1	i	i	PRON
ejpam-1480	96	2	i	i	PRON
ejpam-1480	96	3	,	,	PUNCT
ejpam-1480	96	4	j(m	j(m	PROPN
ejpam-1480	96	5	)	)	PUNCT
ejpam-1480	96	6	a	a	PRON
ejpam-1480	96	7	→	→	SYM
ejpam-1480	96	8	h	h	NOUN
ejpam-1480	97	1	i	i	PRON
ejpam-1480	97	2	i	i	PRON
ejpam-1480	97	3	,	,	PUNCT
ejpam-1480	97	4	j(m)→	j(m)→	NOUN
ejpam-1480	97	5	h	h	NOUN
ejpam-1480	98	1	i	i	PRON
ejpam-1480	98	2	i	i	PRON
ejpam-1480	98	3	,	,	PUNCT
ejpam-1480	98	4	j(m	j(m	PROPN
ejpam-1480	98	5	/	/	SYM
ejpam-1480	98	6	am)→	am)→	ADJ
ejpam-1480	98	7	h	h	NOUN
ejpam-1480	98	8	i+1	i+1	X
ejpam-1480	99	1	i	i	PRON
ejpam-1480	99	2	,	,	PUNCT
ejpam-1480	99	3	j	j	PROPN
ejpam-1480	99	4	(	(	PUNCT
ejpam-1480	99	5	m)→	m)→	VERB
ejpam-1480	99	6	·	·	PUNCT
ejpam-1480	99	7	·	·	PUNCT
ejpam-1480	99	8	·	·	PUNCT
ejpam-1480	99	9	of	of	ADP
ejpam-1480	99	10	local	local	ADJ
ejpam-1480	99	11	cohomology	cohomology	NOUN
ejpam-1480	99	12	modules	module	NOUN
ejpam-1480	99	13	.	.	PUNCT
ejpam-1480	100	1	in	in	ADP
ejpam-1480	100	2	view	view	NOUN
ejpam-1480	100	3	of	of	ADP
ejpam-1480	100	4	the	the	DET
ejpam-1480	100	5	hypothesis	hypothesis	NOUN
ejpam-1480	100	6	and	and	CCONJ
ejpam-1480	100	7	the	the	DET
ejpam-1480	100	8	above	above	ADJ
ejpam-1480	100	9	exact	exact	ADJ
ejpam-1480	100	10	sequence	sequence	NOUN
ejpam-1480	100	11	,	,	PUNCT
ejpam-1480	100	12	h	h	NOUN
ejpam-1480	101	1	i	i	PRON
ejpam-1480	101	2	i	i	PRON
ejpam-1480	101	3	,	,	PUNCT
ejpam-1480	101	4	j(m	j(m	PROPN
ejpam-1480	101	5	/	/	SYM
ejpam-1480	101	6	am	am	NOUN
ejpam-1480	101	7	)	)	PUNCT
ejpam-1480	101	8	=	=	SYM
ejpam-1480	101	9	0	0	NUM
ejpam-1480	101	10	for	for	ADP
ejpam-1480	101	11	all	all	PRON
ejpam-1480	101	12	i	i	PRON
ejpam-1480	101	13	>	>	X
ejpam-1480	101	14	t.	t.	PROPN
ejpam-1480	101	15	since	since	SCONJ
ejpam-1480	101	16	a	a	PRON
ejpam-1480	101	17	is	be	AUX
ejpam-1480	101	18	non	non	ADJ
ejpam-1480	101	19	zero	zero	NUM
ejpam-1480	101	20	-	-	PUNCT
ejpam-1480	101	21	divisor	divisor	NOUN
ejpam-1480	101	22	on	on	ADP
ejpam-1480	101	23	m	m	PROPN
ejpam-1480	101	24	,	,	PUNCT
ejpam-1480	101	25	we	we	PRON
ejpam-1480	101	26	have	have	AUX
ejpam-1480	101	27	dim	dim	VERB
ejpam-1480	101	28	m	m	PRON
ejpam-1480	101	29	/	/	SYM
ejpam-1480	101	30	am	be	AUX
ejpam-1480	101	31	≤	≤	NUM
ejpam-1480	101	32	n−	n−	NOUN
ejpam-1480	101	33	1	1	NUM
ejpam-1480	101	34	,	,	PUNCT
ejpam-1480	101	35	and	and	CCONJ
ejpam-1480	101	36	therefore	therefore	ADV
ejpam-1480	101	37	the	the	DET
ejpam-1480	101	38	inductive	inductive	ADJ
ejpam-1480	101	39	hypothesis	hypothesis	NOUN
ejpam-1480	101	40	implies	imply	VERB
ejpam-1480	101	41	that	that	SCONJ
ejpam-1480	101	42	h	h	NOUN
ejpam-1480	102	1	t	t	NOUN
ejpam-1480	103	1	i	i	PRON
ejpam-1480	103	2	,	,	PUNCT
ejpam-1480	103	3	j(m	j(m	PROPN
ejpam-1480	103	4	/	/	SYM
ejpam-1480	103	5	am)/ah	am)/ah	PROPN
ejpam-1480	103	6	t	t	PROPN
ejpam-1480	103	7	i	i	PRON
ejpam-1480	103	8	,	,	PUNCT
ejpam-1480	103	9	j(m	j(m	PROPN
ejpam-1480	103	10	/	/	SYM
ejpam-1480	103	11	am	am	NOUN
ejpam-1480	103	12	)	)	PUNCT
ejpam-1480	104	1	=	=	SYM
ejpam-1480	104	2	0	0	X
ejpam-1480	104	3	.	.	PUNCT
ejpam-1480	105	1	the	the	DET
ejpam-1480	105	2	above	above	ADJ
ejpam-1480	105	3	exact	exact	ADJ
ejpam-1480	105	4	sequence	sequence	NOUN
ejpam-1480	105	5	implies	imply	VERB
ejpam-1480	105	6	that	that	SCONJ
ejpam-1480	105	7	h	h	NOUN
ejpam-1480	106	1	t	t	NOUN
ejpam-1480	107	1	i	i	PRON
ejpam-1480	107	2	,	,	PUNCT
ejpam-1480	107	3	j(m)/ah	j(m)/ah	PROPN
ejpam-1480	107	4	t	t	PROPN
ejpam-1480	107	5	i	i	PRON
ejpam-1480	107	6	,	,	PUNCT
ejpam-1480	107	7	j(m	j(m	PROPN
ejpam-1480	107	8	)	)	PUNCT
ejpam-1480	107	9	∼=	∼=	PROPN
ejpam-1480	107	10	h	h	NOUN
ejpam-1480	107	11	t	t	NOUN
ejpam-1480	107	12	i	i	PRON
ejpam-1480	107	13	,	,	PUNCT
ejpam-1480	107	14	j(m	j(m	PROPN
ejpam-1480	107	15	/	/	SYM
ejpam-1480	107	16	am	am	PROPN
ejpam-1480	107	17	)	)	PUNCT
ejpam-1480	107	18	.	.	PUNCT
ejpam-1480	108	1	since	since	SCONJ
ejpam-1480	108	2	a	a	DET
ejpam-1480	108	3	∈	∈	PROPN
ejpam-1480	108	4	a	a	PRON
ejpam-1480	108	5	,	,	PUNCT
ejpam-1480	108	6	therefore	therefore	ADV
ejpam-1480	108	7	h	h	PROPN
ejpam-1480	108	8	t	t	PROPN
ejpam-1480	109	1	i	i	PRON
ejpam-1480	109	2	,	,	PUNCT
ejpam-1480	109	3	j(m)/ah	j(m)/ah	PROPN
ejpam-1480	109	4	t	t	PROPN
ejpam-1480	109	5	i	i	PRON
ejpam-1480	109	6	,	,	PUNCT
ejpam-1480	109	7	j(m	j(m	PROPN
ejpam-1480	109	8	)	)	PUNCT
ejpam-1480	109	9	∼=	∼=	PROPN
ejpam-1480	109	10	h	h	NOUN
ejpam-1480	109	11	t	t	NOUN
ejpam-1480	109	12	i	i	PRON
ejpam-1480	109	13	,	,	PUNCT
ejpam-1480	109	14	j(m	j(m	PROPN
ejpam-1480	109	15	/	/	SYM
ejpam-1480	109	16	am)/ah	am)/ah	PROPN
ejpam-1480	109	17	t	t	PROPN
ejpam-1480	110	1	i	i	PRON
ejpam-1480	110	2	,	,	PUNCT
ejpam-1480	110	3	j	j	PROPN
ejpam-1480	110	4	(	(	PUNCT
ejpam-1480	110	5	m	m	NOUN
ejpam-1480	110	6	/	/	SYM
ejpam-1480	110	7	am	am	NOUN
ejpam-1480	110	8	)	)	PUNCT
ejpam-1480	110	9	.	.	PUNCT
ejpam-1480	111	1	the	the	DET
ejpam-1480	111	2	inductive	inductive	ADJ
ejpam-1480	111	3	step	step	NOUN
ejpam-1480	111	4	is	be	AUX
ejpam-1480	111	5	complete	complete	ADJ
ejpam-1480	111	6	.	.	PUNCT
ejpam-1480	112	1	the	the	DET
ejpam-1480	112	2	result	result	NOUN
ejpam-1480	112	3	follows	follow	VERB
ejpam-1480	112	4	by	by	ADP
ejpam-1480	112	5	induction	induction	NOUN
ejpam-1480	112	6	.	.	PUNCT
ejpam-1480	113	1	corollary	corollary	ADJ
ejpam-1480	113	2	1	1	NUM
ejpam-1480	113	3	.	.	PUNCT
ejpam-1480	114	1	let	let	VERB
ejpam-1480	114	2	m	m	PRON
ejpam-1480	114	3	be	be	AUX
ejpam-1480	114	4	a	a	DET
ejpam-1480	114	5	finitely	finitely	ADV
ejpam-1480	114	6	generated	generate	VERB
ejpam-1480	114	7	module	module	NOUN
ejpam-1480	114	8	such	such	ADJ
ejpam-1480	114	9	that	that	DET
ejpam-1480	114	10	dimr	dimr	NOUN
ejpam-1480	114	11	m	m	PROPN
ejpam-1480	114	12	=	=	VERB
ejpam-1480	115	1	n.	n.	NOUN
ejpam-1480	116	1	then	then	ADV
ejpam-1480	116	2	hn	hn	PROPN
ejpam-1480	116	3	i	i	PROPN
ejpam-1480	116	4	,	,	PUNCT
ejpam-1480	116	5	j(m)/ahn	j(m)/ahn	AUX
ejpam-1480	116	6	i	i	PRON
ejpam-1480	116	7	,	,	PUNCT
ejpam-1480	116	8	j(m	j(m	PROPN
ejpam-1480	116	9	)	)	PUNCT
ejpam-1480	116	10	has	have	VERB
ejpam-1480	116	11	finite	finite	ADJ
ejpam-1480	116	12	length	length	NOUN
ejpam-1480	116	13	,	,	PUNCT
ejpam-1480	116	14	for	for	ADP
ejpam-1480	116	15	any	any	DET
ejpam-1480	116	16	a	a	DET
ejpam-1480	116	17	∈	∈	PROPN
ejpam-1480	116	18	w̃(i	w̃(i	PROPN
ejpam-1480	116	19	,	,	PUNCT
ejpam-1480	116	20	j	j	PROPN
ejpam-1480	116	21	)	)	PUNCT
ejpam-1480	116	22	.	.	PUNCT
ejpam-1480	117	1	specially	specially	ADV
ejpam-1480	117	2	,	,	PUNCT
ejpam-1480	117	3	hn	hn	PROPN
ejpam-1480	117	4	i	i	PROPN
ejpam-1480	117	5	,	,	PUNCT
ejpam-1480	117	6	j(m)/ihn	j(m)/ihn	PROPN
ejpam-1480	117	7	i	i	PRON
ejpam-1480	117	8	,	,	PUNCT
ejpam-1480	117	9	j	j	PROPN
ejpam-1480	117	10	(	(	PUNCT
ejpam-1480	117	11	m	m	PROPN
ejpam-1480	117	12	)	)	PUNCT
ejpam-1480	117	13	has	have	VERB
ejpam-1480	117	14	finite	finite	ADJ
ejpam-1480	117	15	length	length	NOUN
ejpam-1480	117	16	.	.	PUNCT
ejpam-1480	118	1	proof	proof	NOUN
ejpam-1480	118	2	.	.	PUNCT
ejpam-1480	119	1	let	let	VERB
ejpam-1480	119	2	a	a	DET
ejpam-1480	119	3	∈	∈	ADJ
ejpam-1480	119	4	w̃(i	w̃(i	PROPN
ejpam-1480	119	5	,	,	PUNCT
ejpam-1480	119	6	j	j	PROPN
ejpam-1480	119	7	)	)	PUNCT
ejpam-1480	119	8	be	be	AUX
ejpam-1480	119	9	fixed	fix	VERB
ejpam-1480	119	10	.	.	PUNCT
ejpam-1480	120	1	if	if	SCONJ
ejpam-1480	120	2	n=	n=	ADJ
ejpam-1480	120	3	0	0	NUM
ejpam-1480	120	4	,	,	PUNCT
ejpam-1480	120	5	then	then	ADV
ejpam-1480	120	6	m	m	PROPN
ejpam-1480	120	7	has	have	VERB
ejpam-1480	120	8	finite	finite	ADJ
ejpam-1480	120	9	length	length	NOUN
ejpam-1480	120	10	and	and	CCONJ
ejpam-1480	120	11	so	so	ADV
ejpam-1480	120	12	γi	γi	INTJ
ejpam-1480	120	13	,	,	PUNCT
ejpam-1480	120	14	j(m)/aγi	j(m)/aγi	VERB
ejpam-1480	120	15	,	,	PUNCT
ejpam-1480	120	16	j(m	j(m	PROPN
ejpam-1480	120	17	)	)	PUNCT
ejpam-1480	120	18	has	have	VERB
ejpam-1480	120	19	finite	finite	ADJ
ejpam-1480	120	20	length	length	NOUN
ejpam-1480	120	21	.	.	PUNCT
ejpam-1480	121	1	now	now	ADV
ejpam-1480	121	2	assume	assume	VERB
ejpam-1480	121	3	that	that	SCONJ
ejpam-1480	121	4	n	n	NOUN
ejpam-1480	121	5	>	>	X
ejpam-1480	121	6	0	0	X
ejpam-1480	121	7	.	.	PUNCT
ejpam-1480	122	1	it	it	PRON
ejpam-1480	122	2	follows	follow	VERB
ejpam-1480	122	3	by	by	ADP
ejpam-1480	122	4	[	[	X
ejpam-1480	122	5	6	6	NUM
ejpam-1480	122	6	,	,	PUNCT
ejpam-1480	122	7	theorem	theorem	VERB
ejpam-1480	122	8	4.7(1	4.7(1	NUM
ejpam-1480	122	9	)	)	PUNCT
ejpam-1480	122	10	]	]	PUNCT
ejpam-1480	122	11	and	and	CCONJ
ejpam-1480	122	12	theorem	theorem	VERB
ejpam-1480	122	13	2	2	NUM
ejpam-1480	122	14	,	,	PUNCT
ejpam-1480	122	15	that	that	SCONJ
ejpam-1480	122	16	hn	hn	PROPN
ejpam-1480	122	17	i	i	PRON
ejpam-1480	122	18	,	,	PUNCT
ejpam-1480	122	19	j(m)/ahn	j(m)/ahn	AUX
ejpam-1480	122	20	i	i	PRON
ejpam-1480	122	21	,	,	PUNCT
ejpam-1480	122	22	j(m	j(m	PROPN
ejpam-1480	122	23	)	)	PUNCT
ejpam-1480	123	1	=	=	SYM
ejpam-1480	123	2	0	0	X
ejpam-1480	123	3	.	.	PUNCT
ejpam-1480	123	4	corollary	corollary	ADJ
ejpam-1480	123	5	2	2	NUM
ejpam-1480	123	6	.	.	PUNCT
ejpam-1480	124	1	let	let	VERB
ejpam-1480	124	2	m	m	PRON
ejpam-1480	124	3	be	be	AUX
ejpam-1480	124	4	finitely	finitely	ADV
ejpam-1480	124	5	generated	generate	VERB
ejpam-1480	124	6	of	of	ADP
ejpam-1480	124	7	finite	finite	ADJ
ejpam-1480	124	8	dimension	dimension	NOUN
ejpam-1480	124	9	such	such	ADJ
ejpam-1480	124	10	that	that	DET
ejpam-1480	124	11	dimr	dimr	NOUN
ejpam-1480	124	12	m	m	PROPN
ejpam-1480	124	13	/	/	SYM
ejpam-1480	124	14	j	j	PROPN
ejpam-1480	124	15	m	m	PROPN
ejpam-1480	124	16	=	=	SYM
ejpam-1480	124	17	d.	d.	PROPN
ejpam-1480	125	1	then	then	ADV
ejpam-1480	125	2	hd+1	hd+1	NUM
ejpam-1480	125	3	i	i	PROPN
ejpam-1480	125	4	,	,	PUNCT
ejpam-1480	125	5	j	j	PROPN
ejpam-1480	125	6	(	(	PUNCT
ejpam-1480	125	7	m)/ahd+1	m)/ahd+1	NOUN
ejpam-1480	125	8	i	i	PROPN
ejpam-1480	125	9	,	,	PUNCT
ejpam-1480	125	10	j	j	PROPN
ejpam-1480	125	11	(	(	PUNCT
ejpam-1480	125	12	m	m	PROPN
ejpam-1480	125	13	)	)	PUNCT
ejpam-1480	125	14	is	be	AUX
ejpam-1480	125	15	finitely	finitely	ADV
ejpam-1480	125	16	generated	generate	VERB
ejpam-1480	125	17	,	,	PUNCT
ejpam-1480	125	18	for	for	ADP
ejpam-1480	125	19	any	any	DET
ejpam-1480	125	20	a	a	DET
ejpam-1480	125	21	∈	∈	PROPN
ejpam-1480	125	22	w̃(i	w̃(i	PROPN
ejpam-1480	125	23	,	,	PUNCT
ejpam-1480	125	24	j	j	PROPN
ejpam-1480	125	25	)	)	PUNCT
ejpam-1480	125	26	.	.	PUNCT
ejpam-1480	126	1	specially	specially	ADV
ejpam-1480	126	2	,	,	PUNCT
ejpam-1480	126	3	hd+1	hd+1	NUM
ejpam-1480	126	4	i	i	PROPN
ejpam-1480	126	5	,	,	PUNCT
ejpam-1480	126	6	j	j	PROPN
ejpam-1480	126	7	(	(	PUNCT
ejpam-1480	126	8	m)/ihd+1	m)/ihd+1	NOUN
ejpam-1480	126	9	i	i	PRON
ejpam-1480	126	10	,	,	PUNCT
ejpam-1480	126	11	j	j	PROPN
ejpam-1480	126	12	(	(	PUNCT
ejpam-1480	126	13	m	m	PROPN
ejpam-1480	126	14	)	)	PUNCT
ejpam-1480	126	15	is	be	AUX
ejpam-1480	126	16	finitely	finitely	ADV
ejpam-1480	126	17	generated	generate	VERB
ejpam-1480	126	18	.	.	PUNCT
ejpam-1480	127	1	proof	proof	NOUN
ejpam-1480	127	2	.	.	PUNCT
ejpam-1480	128	1	let	let	VERB
ejpam-1480	128	2	a	a	DET
ejpam-1480	128	3	∈	∈	ADJ
ejpam-1480	128	4	w̃(i	w̃(i	PROPN
ejpam-1480	128	5	,	,	PUNCT
ejpam-1480	128	6	j	j	PROPN
ejpam-1480	128	7	)	)	PUNCT
ejpam-1480	128	8	be	be	AUX
ejpam-1480	128	9	fixed	fix	VERB
ejpam-1480	128	10	.	.	PUNCT
ejpam-1480	129	1	if	if	SCONJ
ejpam-1480	129	2	d	d	PROPN
ejpam-1480	129	3	=	=	SYM
ejpam-1480	129	4	−1	−1	NOUN
ejpam-1480	129	5	,	,	PUNCT
ejpam-1480	129	6	then	then	ADV
ejpam-1480	129	7	the	the	DET
ejpam-1480	129	8	claim	claim	NOUN
ejpam-1480	129	9	is	be	AUX
ejpam-1480	129	10	trivial	trivial	ADJ
ejpam-1480	129	11	.	.	PUNCT
ejpam-1480	130	1	now	now	ADV
ejpam-1480	130	2	assume	assume	VERB
ejpam-1480	130	3	that	that	SCONJ
ejpam-1480	130	4	d	d	PROPN
ejpam-1480	130	5	≥	≥	NUM
ejpam-1480	130	6	0	0	NUM
ejpam-1480	130	7	.	.	PUNCT
ejpam-1480	131	1	it	it	PRON
ejpam-1480	131	2	follows	follow	VERB
ejpam-1480	131	3	by	by	ADP
ejpam-1480	131	4	[	[	X
ejpam-1480	131	5	6	6	NUM
ejpam-1480	131	6	,	,	PUNCT
ejpam-1480	131	7	theorem	theorem	VERB
ejpam-1480	131	8	4.7(2	4.7(2	NUM
ejpam-1480	131	9	)	)	PUNCT
ejpam-1480	131	10	]	]	PUNCT
ejpam-1480	131	11	and	and	CCONJ
ejpam-1480	131	12	theorem	theorem	VERB
ejpam-1480	131	13	2	2	NUM
ejpam-1480	131	14	,	,	PUNCT
ejpam-1480	131	15	that	that	SCONJ
ejpam-1480	131	16	hd+1	hd+1	NUM
ejpam-1480	131	17	i	i	NOUN
ejpam-1480	131	18	,	,	PUNCT
ejpam-1480	131	19	j	j	PROPN
ejpam-1480	131	20	(	(	PUNCT
ejpam-1480	132	1	m)/ahd+1	m)/ahd+1	NOUN
ejpam-1480	132	2	i	i	PROPN
ejpam-1480	132	3	,	,	PUNCT
ejpam-1480	132	4	j	j	PROPN
ejpam-1480	132	5	(	(	PUNCT
ejpam-1480	132	6	m	m	PROPN
ejpam-1480	132	7	)	)	PUNCT
ejpam-1480	132	8	=	=	SYM
ejpam-1480	132	9	0	0	X
ejpam-1480	132	10	.	.	PUNCT
ejpam-1480	132	11	corollary	corollary	ADJ
ejpam-1480	132	12	3	3	X
ejpam-1480	132	13	.	.	PUNCT
ejpam-1480	133	1	let	let	VERB
ejpam-1480	133	2	r	r	NOUN
ejpam-1480	133	3	be	be	AUX
ejpam-1480	133	4	local	local	ADJ
ejpam-1480	133	5	and	and	CCONJ
ejpam-1480	133	6	m	m	VERB
ejpam-1480	133	7	a	a	DET
ejpam-1480	133	8	finitely	finitely	ADV
ejpam-1480	133	9	generated	generate	VERB
ejpam-1480	133	10	module	module	NOUN
ejpam-1480	133	11	such	such	ADJ
ejpam-1480	133	12	that	that	DET
ejpam-1480	133	13	dimr	dimr	NOUN
ejpam-1480	133	14	m	m	PROPN
ejpam-1480	133	15	/	/	SYM
ejpam-1480	133	16	j	j	PROPN
ejpam-1480	133	17	m	m	PROPN
ejpam-1480	133	18	=	=	SYM
ejpam-1480	133	19	d.	d.	PROPN
ejpam-1480	133	20	then	then	ADV
ejpam-1480	133	21	hd	hd	VERB
ejpam-1480	133	22	i	i	PRON
ejpam-1480	133	23	,	,	PUNCT
ejpam-1480	133	24	j(m)/ahd	j(m)/ahd	ADV
ejpam-1480	133	25	i	i	PRON
ejpam-1480	133	26	,	,	PUNCT
ejpam-1480	133	27	j(m	j(m	PROPN
ejpam-1480	133	28	)	)	PUNCT
ejpam-1480	133	29	is	be	AUX
ejpam-1480	133	30	finitely	finitely	ADV
ejpam-1480	133	31	generated	generate	VERB
ejpam-1480	133	32	,	,	PUNCT
ejpam-1480	133	33	for	for	ADP
ejpam-1480	133	34	any	any	DET
ejpam-1480	133	35	a	a	DET
ejpam-1480	133	36	∈	∈	PROPN
ejpam-1480	133	37	w̃(i	w̃(i	PROPN
ejpam-1480	133	38	,	,	PUNCT
ejpam-1480	133	39	j	j	PROPN
ejpam-1480	133	40	)	)	PUNCT
ejpam-1480	133	41	.	.	PUNCT
ejpam-1480	134	1	in	in	ADP
ejpam-1480	134	2	particular	particular	ADJ
ejpam-1480	134	3	,	,	PUNCT
ejpam-1480	134	4	hd	hd	VERB
ejpam-1480	134	5	i	i	PRON
ejpam-1480	134	6	,	,	PUNCT
ejpam-1480	134	7	j(m)/ihd	j(m)/ihd	PROPN
ejpam-1480	135	1	i	i	PRON
ejpam-1480	135	2	,	,	PUNCT
ejpam-1480	135	3	j	j	PROPN
ejpam-1480	135	4	(	(	PUNCT
ejpam-1480	135	5	m	m	PROPN
ejpam-1480	135	6	)	)	PUNCT
ejpam-1480	135	7	is	be	AUX
ejpam-1480	135	8	finitely	finitely	ADV
ejpam-1480	135	9	generated	generate	VERB
ejpam-1480	135	10	.	.	PUNCT
ejpam-1480	136	1	proof	proof	NOUN
ejpam-1480	136	2	.	.	PUNCT
ejpam-1480	137	1	let	let	VERB
ejpam-1480	137	2	a	a	DET
ejpam-1480	137	3	∈	∈	ADJ
ejpam-1480	137	4	w̃(i	w̃(i	PROPN
ejpam-1480	137	5	,	,	PUNCT
ejpam-1480	137	6	j	j	PROPN
ejpam-1480	137	7	)	)	PUNCT
ejpam-1480	137	8	be	be	AUX
ejpam-1480	137	9	fixed	fix	VERB
ejpam-1480	137	10	.	.	PUNCT
ejpam-1480	138	1	if	if	SCONJ
ejpam-1480	138	2	d	d	PROPN
ejpam-1480	138	3	=	=	SYM
ejpam-1480	138	4	0	0	NUM
ejpam-1480	138	5	,	,	PUNCT
ejpam-1480	138	6	then	then	ADV
ejpam-1480	138	7	the	the	DET
ejpam-1480	138	8	claim	claim	NOUN
ejpam-1480	138	9	is	be	AUX
ejpam-1480	138	10	trivial	trivial	ADJ
ejpam-1480	138	11	.	.	PUNCT
ejpam-1480	139	1	now	now	ADV
ejpam-1480	139	2	assume	assume	VERB
ejpam-1480	139	3	that	that	SCONJ
ejpam-1480	139	4	d	d	X
ejpam-1480	139	5	>	>	X
ejpam-1480	139	6	0	0	X
ejpam-1480	139	7	.	.	PUNCT
ejpam-1480	140	1	it	it	PRON
ejpam-1480	140	2	follows	follow	VERB
ejpam-1480	140	3	by	by	ADP
ejpam-1480	140	4	[	[	X
ejpam-1480	140	5	6	6	NUM
ejpam-1480	140	6	,	,	PUNCT
ejpam-1480	140	7	theorem	theorem	VERB
ejpam-1480	140	8	4.3	4.3	NUM
ejpam-1480	140	9	]	]	PUNCT
ejpam-1480	140	10	and	and	CCONJ
ejpam-1480	140	11	theorem	theorem	VERB
ejpam-1480	140	12	2	2	NUM
ejpam-1480	140	13	,	,	PUNCT
ejpam-1480	140	14	that	that	PRON
ejpam-1480	140	15	hd	hd	VERB
ejpam-1480	140	16	i	i	PRON
ejpam-1480	140	17	,	,	PUNCT
ejpam-1480	140	18	j(m)/ahd	j(m)/ahd	ADV
ejpam-1480	140	19	i	i	PRON
ejpam-1480	140	20	,	,	PUNCT
ejpam-1480	140	21	j(m	j(m	PROPN
ejpam-1480	140	22	)	)	PUNCT
ejpam-1480	141	1	=	=	SYM
ejpam-1480	141	2	0	0	X
ejpam-1480	141	3	.	.	PUNCT
ejpam-1480	142	1	proposition	proposition	NOUN
ejpam-1480	142	2	1	1	NUM
ejpam-1480	142	3	.	.	PUNCT
ejpam-1480	143	1	let	let	VERB
ejpam-1480	143	2	r	r	NOUN
ejpam-1480	143	3	be	be	AUX
ejpam-1480	143	4	local	local	ADJ
ejpam-1480	143	5	,	,	PUNCT
ejpam-1480	143	6	m	m	AUX
ejpam-1480	143	7	finitely	finitely	ADV
ejpam-1480	143	8	generated	generate	VERB
ejpam-1480	143	9	and	and	CCONJ
ejpam-1480	143	10	t	t	PROPN
ejpam-1480	143	11	a	a	DET
ejpam-1480	143	12	non	non	ADJ
ejpam-1480	143	13	-	-	ADJ
ejpam-1480	143	14	negative	negative	ADJ
ejpam-1480	143	15	integer	integer	NOUN
ejpam-1480	143	16	.	.	PUNCT
ejpam-1480	144	1	if	if	SCONJ
ejpam-1480	144	2	h	h	PRON
ejpam-1480	144	3	i	i	PRON
ejpam-1480	144	4	i	i	PRON
ejpam-1480	144	5	,	,	PUNCT
ejpam-1480	144	6	j(m	j(m	PROPN
ejpam-1480	144	7	)	)	PUNCT
ejpam-1480	144	8	is	be	AUX
ejpam-1480	144	9	finitely	finitely	ADV
ejpam-1480	144	10	generated	generate	VERB
ejpam-1480	144	11	,	,	PUNCT
ejpam-1480	144	12	for	for	ADP
ejpam-1480	144	13	all	all	PRON
ejpam-1480	144	14	i	i	PRON
ejpam-1480	144	15	>	>	X
ejpam-1480	144	16	t	t	PROPN
ejpam-1480	145	1	,	,	PUNCT
ejpam-1480	145	2	then	then	ADV
ejpam-1480	145	3	h	h	NOUN
ejpam-1480	145	4	i	i	PRON
ejpam-1480	145	5	i	i	PRON
ejpam-1480	145	6	,	,	PUNCT
ejpam-1480	145	7	j(m	j(m	PROPN
ejpam-1480	145	8	)	)	PUNCT
ejpam-1480	146	1	=	=	SYM
ejpam-1480	146	2	0	0	NUM
ejpam-1480	146	3	,	,	PUNCT
ejpam-1480	146	4	for	for	ADP
ejpam-1480	146	5	all	all	DET
ejpam-1480	146	6	i	i	PRON
ejpam-1480	146	7	>	>	X
ejpam-1480	146	8	t.	t.	PROPN
ejpam-1480	146	9	references	reference	NOUN
ejpam-1480	146	10	58	58	NUM
ejpam-1480	146	11	proof	proof	NOUN
ejpam-1480	146	12	.	.	PUNCT
ejpam-1480	147	1	we	we	PRON
ejpam-1480	147	2	may	may	AUX
ejpam-1480	147	3	assume	assume	VERB
ejpam-1480	147	4	that	that	SCONJ
ejpam-1480	147	5	i	i	PRON
ejpam-1480	147	6	6=	6=	SYM
ejpam-1480	147	7	r	r	NOUN
ejpam-1480	147	8	,	,	PUNCT
ejpam-1480	147	9	otherwise	otherwise	ADV
ejpam-1480	147	10	γi	γi	X
ejpam-1480	147	11	,	,	PUNCT
ejpam-1480	147	12	j	j	PROPN
ejpam-1480	147	13	is	be	AUX
ejpam-1480	147	14	identity	identity	NOUN
ejpam-1480	147	15	functor	functor	NOUN
ejpam-1480	147	16	.	.	PUNCT
ejpam-1480	148	1	proposition	proposition	NOUN
ejpam-1480	148	2	4.10	4.10	NUM
ejpam-1480	148	3	,	,	PUNCT
ejpam-1480	148	4	in	in	ADP
ejpam-1480	148	5	[	[	PUNCT
ejpam-1480	148	6	6	6	NUM
ejpam-1480	148	7	]	]	PUNCT
ejpam-1480	148	8	,	,	PUNCT
ejpam-1480	148	9	says	say	VERB
ejpam-1480	148	10	that	that	SCONJ
ejpam-1480	149	1	h	h	NOUN
ejpam-1480	150	1	i	i	PRON
ejpam-1480	150	2	i	i	PRON
ejpam-1480	150	3	,	,	PUNCT
ejpam-1480	150	4	j(m	j(m	PROPN
ejpam-1480	150	5	)	)	PUNCT
ejpam-1480	151	1	=	=	SYM
ejpam-1480	151	2	0	0	NUM
ejpam-1480	151	3	,	,	PUNCT
ejpam-1480	151	4	for	for	ADP
ejpam-1480	151	5	all	all	DET
ejpam-1480	151	6	i	i	PRON
ejpam-1480	151	7	>	>	X
ejpam-1480	151	8	ara(ir	ara(ir	NUM
ejpam-1480	151	9	)	)	PUNCT
ejpam-1480	151	10	,	,	PUNCT
ejpam-1480	151	11	where	where	SCONJ
ejpam-1480	151	12	r	r	NOUN
ejpam-1480	151	13	=	=	PUNCT
ejpam-1480	151	14	r/	r/	ADV
ejpam-1480	151	15	p	p	X
ejpam-1480	151	16	j	j	PROPN
ejpam-1480	151	17	+	+	NOUN
ejpam-1480	151	18	annr(m	annr(m	NOUN
ejpam-1480	151	19	)	)	PUNCT
ejpam-1480	151	20	.	.	PUNCT
ejpam-1480	152	1	let	let	VERB
ejpam-1480	152	2	s	s	PRON
ejpam-1480	152	3	=	=	VERB
ejpam-1480	152	4	ara(ir	ara(ir	X
ejpam-1480	152	5	)	)	PUNCT
ejpam-1480	152	6	.	.	PUNCT
ejpam-1480	153	1	when	when	SCONJ
ejpam-1480	153	2	t	t	PROPN
ejpam-1480	153	3	≥	≥	NOUN
ejpam-1480	153	4	s	s	PART
ejpam-1480	153	5	,	,	PUNCT
ejpam-1480	153	6	there	there	PRON
ejpam-1480	153	7	is	be	VERB
ejpam-1480	153	8	nothing	nothing	PRON
ejpam-1480	153	9	to	to	PART
ejpam-1480	153	10	prove	prove	VERB
ejpam-1480	153	11	.	.	PUNCT
ejpam-1480	154	1	now	now	ADV
ejpam-1480	154	2	,	,	PUNCT
ejpam-1480	154	3	assume	assume	VERB
ejpam-1480	154	4	that	that	SCONJ
ejpam-1480	154	5	t	t	PROPN
ejpam-1480	154	6	<	<	X
ejpam-1480	154	7	s.	s.	PROPN
ejpam-1480	154	8	in	in	ADP
ejpam-1480	154	9	view	view	NOUN
ejpam-1480	154	10	of	of	ADP
ejpam-1480	154	11	theorem	theorem	NOUN
ejpam-1480	154	12	2	2	NUM
ejpam-1480	154	13	,	,	PUNCT
ejpam-1480	154	14	we	we	PRON
ejpam-1480	154	15	have	have	VERB
ejpam-1480	154	16	hs	hs	PROPN
ejpam-1480	154	17	i	i	PROPN
ejpam-1480	154	18	,	,	PUNCT
ejpam-1480	154	19	j(m)/ihs	j(m)/ihs	X
ejpam-1480	155	1	i	i	PRON
ejpam-1480	155	2	,	,	PUNCT
ejpam-1480	155	3	j	j	PROPN
ejpam-1480	155	4	(	(	PUNCT
ejpam-1480	155	5	m	m	PROPN
ejpam-1480	155	6	)	)	PUNCT
ejpam-1480	155	7	=	=	SYM
ejpam-1480	155	8	0	0	NUM
ejpam-1480	155	9	,	,	PUNCT
ejpam-1480	155	10	so	so	ADV
ejpam-1480	155	11	nakayama	nakayama	PROPN
ejpam-1480	155	12	’s	’s	PART
ejpam-1480	155	13	lemma	lemma	PROPN
ejpam-1480	155	14	shows	show	VERB
ejpam-1480	155	15	that	that	SCONJ
ejpam-1480	155	16	hs	hs	PROPN
ejpam-1480	155	17	i	i	PROPN
ejpam-1480	155	18	,	,	PUNCT
ejpam-1480	155	19	j(m	j(m	PROPN
ejpam-1480	155	20	)	)	PUNCT
ejpam-1480	155	21	=	=	SYM
ejpam-1480	156	1	0	0	X
ejpam-1480	156	2	.	.	PUNCT
ejpam-1480	156	3	by	by	ADP
ejpam-1480	156	4	keeping	keep	VERB
ejpam-1480	156	5	this	this	DET
ejpam-1480	156	6	process	process	NOUN
ejpam-1480	156	7	,	,	PUNCT
ejpam-1480	156	8	we	we	PRON
ejpam-1480	156	9	deduce	deduce	VERB
ejpam-1480	156	10	that	that	SCONJ
ejpam-1480	156	11	h	h	NOUN
ejpam-1480	157	1	i	i	PRON
ejpam-1480	157	2	i	i	PRON
ejpam-1480	157	3	,	,	PUNCT
ejpam-1480	157	4	j(m	j(m	PROPN
ejpam-1480	157	5	)	)	PUNCT
ejpam-1480	158	1	=	=	SYM
ejpam-1480	158	2	0	0	NUM
ejpam-1480	158	3	,	,	PUNCT
ejpam-1480	158	4	for	for	ADP
ejpam-1480	158	5	all	all	PRON
ejpam-1480	158	6	i	i	PRON
ejpam-1480	158	7	>	>	X
ejpam-1480	158	8	t.	t.	PROPN
ejpam-1480	158	9	corollary	corollary	ADJ
ejpam-1480	158	10	4	4	NUM
ejpam-1480	158	11	.	.	PUNCT
ejpam-1480	159	1	let	let	VERB
ejpam-1480	159	2	r	r	NOUN
ejpam-1480	159	3	be	be	AUX
ejpam-1480	159	4	local	local	ADJ
ejpam-1480	159	5	with	with	ADP
ejpam-1480	159	6	dim	dim	ADJ
ejpam-1480	159	7	r	r	NOUN
ejpam-1480	159	8	/	/	SYM
ejpam-1480	159	9	i	i	PROPN
ejpam-1480	159	10	+	+	NUM
ejpam-1480	159	11	j	j	PROPN
ejpam-1480	159	12	=	=	SYM
ejpam-1480	159	13	0	0	PROPN
ejpam-1480	159	14	and	and	CCONJ
ejpam-1480	159	15	m	m	AUX
ejpam-1480	159	16	finitely	finitely	ADV
ejpam-1480	159	17	generated	generate	VERB
ejpam-1480	159	18	.	.	PUNCT
ejpam-1480	160	1	then	then	ADV
ejpam-1480	160	2	hd	hd	VERB
ejpam-1480	160	3	i	i	PRON
ejpam-1480	160	4	,	,	PUNCT
ejpam-1480	160	5	j(m	j(m	PROPN
ejpam-1480	160	6	)	)	PUNCT
ejpam-1480	160	7	is	be	AUX
ejpam-1480	160	8	not	not	PART
ejpam-1480	160	9	finitely	finitely	ADV
ejpam-1480	160	10	generated	generate	VERB
ejpam-1480	160	11	,	,	PUNCT
ejpam-1480	160	12	where	where	SCONJ
ejpam-1480	160	13	dimr	dimr	NOUN
ejpam-1480	160	14	m	m	PROPN
ejpam-1480	160	15	/	/	SYM
ejpam-1480	160	16	j	j	PROPN
ejpam-1480	160	17	m	m	NOUN
ejpam-1480	160	18	=	=	SYM
ejpam-1480	161	1	d	d	X
ejpam-1480	161	2	>	>	X
ejpam-1480	161	3	0	0	X
ejpam-1480	161	4	.	.	PUNCT
ejpam-1480	161	5	proof	proof	NOUN
ejpam-1480	161	6	.	.	PUNCT
ejpam-1480	162	1	note	note	VERB
ejpam-1480	162	2	that	that	PRON
ejpam-1480	162	3	sup{i	sup{i	VERB
ejpam-1480	162	4	:	:	PUNCT
ejpam-1480	163	1	h	h	NOUN
ejpam-1480	164	1	i	i	PRON
ejpam-1480	164	2	i	i	PRON
ejpam-1480	164	3	,	,	PUNCT
ejpam-1480	164	4	j(m	j(m	PROPN
ejpam-1480	164	5	)	)	PUNCT
ejpam-1480	165	1	6=	6=	ADP
ejpam-1480	165	2	0}=	0}=	PROPN
ejpam-1480	165	3	d	d	X
ejpam-1480	165	4	,	,	PUNCT
ejpam-1480	165	5	by	by	ADP
ejpam-1480	165	6	[	[	X
ejpam-1480	165	7	6	6	NUM
ejpam-1480	165	8	,	,	PUNCT
ejpam-1480	165	9	theorem	theorem	VERB
ejpam-1480	165	10	4.5	4.5	NUM
ejpam-1480	165	11	]	]	PUNCT
ejpam-1480	165	12	.	.	PUNCT
ejpam-1480	166	1	now	now	ADV
ejpam-1480	166	2	the	the	DET
ejpam-1480	166	3	claim	claim	NOUN
ejpam-1480	166	4	follows	follow	VERB
ejpam-1480	166	5	by	by	ADP
ejpam-1480	166	6	proposition	proposition	NOUN
ejpam-1480	166	7	1	1	NUM
ejpam-1480	166	8	.	.	PUNCT
ejpam-1480	167	1	references	reference	NOUN
ejpam-1480	167	2	[	[	X
ejpam-1480	167	3	1	1	NUM
ejpam-1480	167	4	]	]	PUNCT
ejpam-1480	167	5	m	m	NOUN
ejpam-1480	167	6	brodmann	brodmann	NOUN
ejpam-1480	167	7	and	and	CCONJ
ejpam-1480	167	8	r	r	NOUN
ejpam-1480	167	9	sharp	sharp	ADJ
ejpam-1480	167	10	.	.	PUNCT
ejpam-1480	168	1	local	local	ADJ
ejpam-1480	168	2	cohomology	cohomology	NOUN
ejpam-1480	168	3	:	:	PUNCT
ejpam-1480	168	4	an	an	DET
ejpam-1480	168	5	algebraic	algebraic	ADJ
ejpam-1480	168	6	introduction	introduction	NOUN
ejpam-1480	168	7	with	with	ADP
ejpam-1480	168	8	geometric	geometric	ADJ
ejpam-1480	168	9	applications	application	NOUN
ejpam-1480	168	10	,	,	PUNCT
ejpam-1480	168	11	cambridge	cambridge	PROPN
ejpam-1480	168	12	university	university	PROPN
ejpam-1480	168	13	press	press	PROPN
ejpam-1480	168	14	,	,	PUNCT
ejpam-1480	168	15	cambridge	cambridge	PROPN
ejpam-1480	168	16	,	,	PUNCT
ejpam-1480	168	17	1998	1998	NUM
ejpam-1480	168	18	.	.	PUNCT
ejpam-1480	169	1	[	[	X
ejpam-1480	169	2	2	2	NUM
ejpam-1480	169	3	]	]	X
ejpam-1480	169	4	l	l	PROPN
ejpam-1480	169	5	chu	chu	PROPN
ejpam-1480	169	6	.	.	PUNCT
ejpam-1480	170	1	top	top	ADJ
ejpam-1480	170	2	local	local	ADJ
ejpam-1480	170	3	cohomology	cohomology	NOUN
ejpam-1480	170	4	modules	module	NOUN
ejpam-1480	170	5	with	with	ADP
ejpam-1480	170	6	respect	respect	NOUN
ejpam-1480	170	7	to	to	ADP
ejpam-1480	170	8	a	a	DET
ejpam-1480	170	9	pair	pair	NOUN
ejpam-1480	170	10	of	of	ADP
ejpam-1480	170	11	ideals	ideal	NOUN
ejpam-1480	170	12	,	,	PUNCT
ejpam-1480	170	13	proc	proc	NOUN
ejpam-1480	170	14	.	.	PUNCT
ejpam-1480	171	1	amer	amer	PROPN
ejpam-1480	171	2	.	.	PUNCT
ejpam-1480	171	3	math	math	PROPN
ejpam-1480	171	4	.	.	PUNCT
ejpam-1480	172	1	soc	soc	PROPN
ejpam-1480	172	2	.	.	PUNCT
ejpam-1480	172	3	,	,	PUNCT
ejpam-1480	172	4	139:777	139:777	PROPN
ejpam-1480	172	5	-	-	PUNCT
ejpam-1480	172	6	782	782	NUM
ejpam-1480	172	7	,	,	PUNCT
ejpam-1480	172	8	2011	2011	NUM
ejpam-1480	172	9	.	.	PUNCT
ejpam-1480	173	1	[	[	X
ejpam-1480	173	2	3	3	NUM
ejpam-1480	173	3	]	]	X
ejpam-1480	173	4	l	l	NOUN
ejpam-1480	173	5	chu	chu	PROPN
ejpam-1480	173	6	and	and	CCONJ
ejpam-1480	173	7	q	q	PROPN
ejpam-1480	173	8	wang	wang	PROPN
ejpam-1480	173	9	.	.	PUNCT
ejpam-1480	174	1	some	some	DET
ejpam-1480	174	2	results	result	NOUN
ejpam-1480	174	3	on	on	ADP
ejpam-1480	174	4	local	local	ADJ
ejpam-1480	174	5	cohomology	cohomology	NOUN
ejpam-1480	174	6	modules	module	NOUN
ejpam-1480	174	7	defined	define	VERB
ejpam-1480	174	8	by	by	ADP
ejpam-1480	174	9	a	a	DET
ejpam-1480	174	10	pair	pair	NOUN
ejpam-1480	174	11	of	of	ADP
ejpam-1480	174	12	ideals	ideal	NOUN
ejpam-1480	174	13	,	,	PUNCT
ejpam-1480	174	14	j.	j.	PROPN
ejpam-1480	174	15	math	math	PROPN
ejpam-1480	174	16	.	.	PUNCT
ejpam-1480	175	1	kyoto	kyoto	PROPN
ejpam-1480	175	2	univ	univ	PROPN
ejpam-1480	175	3	.	.	PROPN
ejpam-1480	175	4	,	,	PUNCT
ejpam-1480	175	5	49:193	49:193	NUM
ejpam-1480	175	6	-	-	SYM
ejpam-1480	175	7	200	200	NUM
ejpam-1480	175	8	,	,	PUNCT
ejpam-1480	175	9	2009	2009	NUM
ejpam-1480	175	10	.	.	PUNCT
ejpam-1480	176	1	[	[	X
ejpam-1480	176	2	4	4	NUM
ejpam-1480	176	3	]	]	X
ejpam-1480	176	4	l	l	NOUN
ejpam-1480	176	5	melkersson	melkersson	PROPN
ejpam-1480	176	6	.	.	PUNCT
ejpam-1480	177	1	modules	module	NOUN
ejpam-1480	177	2	cofinite	cofinite	VERB
ejpam-1480	177	3	with	with	ADP
ejpam-1480	177	4	respect	respect	NOUN
ejpam-1480	177	5	to	to	ADP
ejpam-1480	177	6	an	an	DET
ejpam-1480	177	7	ideal	ideal	NOUN
ejpam-1480	177	8	,	,	PUNCT
ejpam-1480	177	9	j.	j.	PROPN
ejpam-1480	177	10	algebra	algebra	PROPN
ejpam-1480	177	11	,	,	PUNCT
ejpam-1480	177	12	285:649	285:649	NOUN
ejpam-1480	177	13	-	-	PUNCT
ejpam-1480	177	14	668	668	NUM
ejpam-1480	177	15	,	,	PUNCT
ejpam-1480	177	16	2005	2005	NUM
ejpam-1480	177	17	.	.	PUNCT
ejpam-1480	178	1	[	[	X
ejpam-1480	178	2	5	5	X
ejpam-1480	178	3	]	]	X
ejpam-1480	178	4	sh	sh	PROPN
ejpam-1480	178	5	payrovi	payrovi	PROPN
ejpam-1480	178	6	and	and	CCONJ
ejpam-1480	178	7	m	m	PROPN
ejpam-1480	178	8	parsa	parsa	PROPN
ejpam-1480	178	9	.	.	PUNCT
ejpam-1480	179	1	artinianness	artinianness	ADJ
ejpam-1480	179	2	of	of	ADP
ejpam-1480	179	3	local	local	ADJ
ejpam-1480	179	4	cohomology	cohomology	NOUN
ejpam-1480	179	5	modules	module	NOUN
ejpam-1480	179	6	defined	define	VERB
ejpam-1480	179	7	by	by	ADP
ejpam-1480	179	8	a	a	DET
ejpam-1480	179	9	pair	pair	NOUN
ejpam-1480	179	10	of	of	ADP
ejpam-1480	179	11	ideals	ideal	NOUN
ejpam-1480	179	12	,	,	PUNCT
ejpam-1480	179	13	to	to	PART
ejpam-1480	179	14	appear	appear	VERB
ejpam-1480	179	15	in	in	ADP
ejpam-1480	179	16	bull	bull	NOUN
ejpam-1480	179	17	.	.	PUNCT
ejpam-1480	180	1	malays	malays	PROPN
ejpam-1480	180	2	.	.	PUNCT
ejpam-1480	181	1	math	math	NOUN
ejpam-1480	181	2	.	.	PUNCT
ejpam-1480	182	1	sci	sci	PROPN
ejpam-1480	182	2	.	.	PROPN
ejpam-1480	182	3	soc	soc	PROPN
ejpam-1480	182	4	.	.	PUNCT
ejpam-1480	183	1	(	(	PUNCT
ejpam-1480	183	2	2	2	NUM
ejpam-1480	183	3	)	)	PUNCT
ejpam-1480	183	4	.	.	PUNCT
ejpam-1480	184	1	[	[	X
ejpam-1480	184	2	6	6	NUM
ejpam-1480	184	3	]	]	X
ejpam-1480	184	4	r	r	NOUN
ejpam-1480	184	5	takahashi	takahashi	PROPN
ejpam-1480	184	6	,	,	PUNCT
ejpam-1480	184	7	y	y	PROPN
ejpam-1480	184	8	yoshino	yoshino	NOUN
ejpam-1480	184	9	and	and	CCONJ
ejpam-1480	184	10	t	t	PROPN
ejpam-1480	184	11	yoshizawa	yoshizawa	PROPN
ejpam-1480	184	12	.	.	PUNCT
ejpam-1480	185	1	local	local	ADJ
ejpam-1480	185	2	cohomology	cohomology	NOUN
ejpam-1480	185	3	based	base	VERB
ejpam-1480	185	4	on	on	ADP
ejpam-1480	185	5	a	a	DET
ejpam-1480	185	6	nonclosed	nonclosed	ADJ
ejpam-1480	185	7	support	support	NOUN
ejpam-1480	185	8	defined	define	VERB
ejpam-1480	185	9	by	by	ADP
ejpam-1480	185	10	a	a	DET
ejpam-1480	185	11	pair	pair	NOUN
ejpam-1480	185	12	of	of	ADP
ejpam-1480	185	13	ideals	ideal	NOUN
ejpam-1480	185	14	,	,	PUNCT
ejpam-1480	185	15	j.	j.	PROPN
ejpam-1480	185	16	pure	pure	PROPN
ejpam-1480	185	17	appl	appl	PROPN
ejpam-1480	185	18	.	.	PUNCT
ejpam-1480	186	1	algebra	algebra	NOUN
ejpam-1480	186	2	,	,	PUNCT
ejpam-1480	186	3	213:582	213:582	PROPN
ejpam-1480	186	4	-	-	SYM
ejpam-1480	186	5	600	600	NUM
ejpam-1480	186	6	,	,	PUNCT
ejpam-1480	186	7	2009	2009	NUM
ejpam-1480	186	8	.	.	PUNCT
ejpam-1480	187	1	[	[	X
ejpam-1480	187	2	7	7	X
ejpam-1480	187	3	]	]	X
ejpam-1480	187	4	a	a	DET
ejpam-1480	187	5	tehranian	tehranian	NOUN
ejpam-1480	187	6	and	and	CCONJ
ejpam-1480	187	7	a	a	DET
ejpam-1480	187	8	talemi	talemi	NOUN
ejpam-1480	187	9	.	.	PUNCT
ejpam-1480	188	1	cofiniteness	cofiniteness	NOUN
ejpam-1480	188	2	of	of	ADP
ejpam-1480	188	3	local	local	ADJ
ejpam-1480	188	4	cohomology	cohomology	NOUN
ejpam-1480	188	5	based	base	VERB
ejpam-1480	188	6	on	on	ADP
ejpam-1480	188	7	a	a	DET
ejpam-1480	188	8	nonclosed	nonclosed	ADJ
ejpam-1480	188	9	support	support	NOUN
ejpam-1480	188	10	defined	define	VERB
ejpam-1480	188	11	by	by	ADP
ejpam-1480	188	12	a	a	DET
ejpam-1480	188	13	pair	pair	NOUN
ejpam-1480	188	14	of	of	ADP
ejpam-1480	188	15	ideals	ideal	NOUN
ejpam-1480	188	16	,	,	PUNCT
ejpam-1480	188	17	bull	bull	NOUN
ejpam-1480	188	18	.	.	PUNCT
ejpam-1480	189	1	iranian	iranian	ADJ
ejpam-1480	189	2	math	math	PROPN
ejpam-1480	189	3	.	.	PUNCT
ejpam-1480	190	1	soc	soc	PROPN
ejpam-1480	190	2	.	.	PROPN
ejpam-1480	190	3	,	,	PUNCT
ejpam-1480	190	4	36:145	36:145	NUM
ejpam-1480	190	5	-	-	SYM
ejpam-1480	190	6	155	155	NUM
ejpam-1480	190	7	,	,	PUNCT
ejpam-1480	190	8	2010	2010	NUM
ejpam-1480	190	9	.	.	PUNCT