id	sid	tid	token	lemma	pos
fb494745m0v	1	1	given	give	VERB
fb494745m0v	1	2	a	a	DET
fb494745m0v	1	3	(	(	PUNCT
fb494745m0v	1	4	partial	partial	ADJ
fb494745m0v	1	5	)	)	PUNCT
fb494745m0v	1	6	flag	flag	NOUN
fb494745m0v	1	7	variety	variety	NOUN
fb494745m0v	1	8	over	over	ADP
fb494745m0v	1	9	algebraically	algebraically	ADV
fb494745m0v	1	10	closed	close	VERB
fb494745m0v	1	11	field	field	NOUN
fb494745m0v	1	12	k	k	PROPN
fb494745m0v	1	13	,	,	PUNCT
fb494745m0v	1	14	a	a	DET
fb494745m0v	1	15	fundamental	fundamental	ADJ
fb494745m0v	1	16	problem	problem	NOUN
fb494745m0v	1	17	is	be	AUX
fb494745m0v	1	18	to	to	PART
fb494745m0v	1	19	determine	determine	VERB
fb494745m0v	1	20	the	the	DET
fb494745m0v	1	21	sheaf	sheaf	ADJ
fb494745m0v	1	22	cohomology	cohomology	NOUN
fb494745m0v	1	23	groups	group	NOUN
fb494745m0v	1	24	of	of	ADP
fb494745m0v	1	25	line	line	NOUN
fb494745m0v	1	26	bundles	bundle	NOUN
fb494745m0v	1	27	on	on	ADP
fb494745m0v	1	28	it	it	PRON
fb494745m0v	1	29	.	.	PUNCT
fb494745m0v	2	1	in	in	ADP
fb494745m0v	2	2	characteristic	characteristic	ADJ
fb494745m0v	2	3	zero	zero	NUM
fb494745m0v	2	4	,	,	PUNCT
fb494745m0v	2	5	a	a	DET
fb494745m0v	2	6	complete	complete	ADJ
fb494745m0v	2	7	answer	answer	NOUN
fb494745m0v	2	8	is	be	AUX
fb494745m0v	2	9	given	give	VERB
fb494745m0v	2	10	by	by	ADP
fb494745m0v	2	11	the	the	DET
fb494745m0v	2	12	borel	borel	PROPN
fb494745m0v	2	13	-	-	PUNCT
fb494745m0v	2	14	weil	weil	PROPN
fb494745m0v	2	15	-	-	PUNCT
fb494745m0v	2	16	bott	bott	NOUN
fb494745m0v	2	17	theorem	theorem	NOUN
fb494745m0v	2	18	.	.	PUNCT
fb494745m0v	3	1	over	over	ADP
fb494745m0v	3	2	fields	field	NOUN
fb494745m0v	3	3	of	of	ADP
fb494745m0v	3	4	positive	positive	ADJ
fb494745m0v	3	5	characteristic	characteristic	NOUN
fb494745m0v	3	6	,	,	PUNCT
fb494745m0v	3	7	results	result	NOUN
fb494745m0v	3	8	such	such	ADJ
fb494745m0v	3	9	as	as	ADP
fb494745m0v	3	10	kempf	kempf	NOUN
fb494745m0v	3	11	's	's	PART
fb494745m0v	3	12	vanishing	vanish	VERB
fb494745m0v	3	13	theorem	theorem	NOUN
fb494745m0v	3	14	and	and	CCONJ
fb494745m0v	3	15	anderson	anderson	PROPN
fb494745m0v	3	16	's	's	PART
fb494745m0v	3	17	characterization	characterization	NOUN
fb494745m0v	3	18	of	of	ADP
fb494745m0v	3	19	(	(	PUNCT
fb494745m0v	3	20	non)vanishing	non)vanishing	PROPN
fb494745m0v	3	21	of	of	ADP
fb494745m0v	3	22	h1	h1	PROPN
fb494745m0v	3	23	provide	provide	VERB
fb494745m0v	3	24	partial	partial	ADJ
fb494745m0v	3	25	answers	answer	NOUN
fb494745m0v	3	26	.	.	PUNCT
fb494745m0v	4	1	however	however	ADV
fb494745m0v	4	2	,	,	PUNCT
fb494745m0v	4	3	the	the	DET
fb494745m0v	4	4	problem	problem	NOUN
fb494745m0v	4	5	still	still	ADV
fb494745m0v	4	6	remains	remain	VERB
fb494745m0v	4	7	largely	largely	ADV
fb494745m0v	4	8	unknown	unknown	ADJ
fb494745m0v	4	9	in	in	ADP
fb494745m0v	4	10	positive	positive	ADJ
fb494745m0v	4	11	characteristic	characteristic	NOUN
fb494745m0v	4	12	.	.	PUNCT
fb494745m0v	5	1	this	this	DET
fb494745m0v	5	2	thesis	thesis	NOUN
fb494745m0v	5	3	is	be	AUX
fb494745m0v	5	4	dedicated	dedicate	VERB
fb494745m0v	5	5	to	to	ADP
fb494745m0v	5	6	characterizing	characterize	VERB
fb494745m0v	5	7	the	the	DET
fb494745m0v	5	8	(	(	PUNCT
fb494745m0v	5	9	non)vanishing	non)vanishing	PROPN
fb494745m0v	5	10	of	of	ADP
fb494745m0v	5	11	cohomology	cohomology	NOUN
fb494745m0v	5	12	of	of	ADP
fb494745m0v	5	13	line	line	NOUN
fb494745m0v	5	14	bundles	bundle	NOUN
fb494745m0v	5	15	on	on	ADP
fb494745m0v	5	16	the	the	DET
fb494745m0v	5	17	incidence	incidence	NOUN
fb494745m0v	5	18	correspondence	correspondence	NOUN
fb494745m0v	5	19	x	x	PUNCT
fb494745m0v	5	20	=	=	X
fb494745m0v	5	21	{	{	PUNCT
fb494745m0v	5	22	(	(	PUNCT
fb494745m0v	5	23	p	p	PROPN
fb494745m0v	5	24	,	,	PUNCT
fb494745m0v	5	25	h	h	PROPN
fb494745m0v	5	26	)	)	PUNCT
fb494745m0v	5	27	∈	∈	PUNCT
fb494745m0v	6	1	ℙv	ℙv	PROPN
fb494745m0v	6	2	×	×	PUNCT
fb494745m0v	7	1	ℙvv	ℙvv	NOUN
fb494745m0v	7	2	:	:	PUNCT
fb494745m0v	7	3	p	p	PROPN
fb494745m0v	7	4	∈	∈	X
fb494745m0v	7	5	h	h	PROPN
fb494745m0v	7	6	}	}	PUNCT
fb494745m0v	7	7	,	,	PUNCT
fb494745m0v	7	8	where	where	SCONJ
fb494745m0v	7	9	v	v	NOUN
fb494745m0v	7	10	is	be	AUX
fb494745m0v	7	11	a	a	DET
fb494745m0v	7	12	vector	vector	NOUN
fb494745m0v	7	13	space	space	NOUN
fb494745m0v	7	14	of	of	ADP
fb494745m0v	7	15	dimension	dimension	NOUN
fb494745m0v	7	16	n	n	CCONJ
fb494745m0v	7	17	≥	≥	X
fb494745m0v	7	18	3	3	NUM
fb494745m0v	7	19	over	over	ADP
fb494745m0v	7	20	an	an	DET
fb494745m0v	7	21	algebraically	algebraically	ADV
fb494745m0v	7	22	closed	close	VERB
fb494745m0v	7	23	field	field	NOUN
fb494745m0v	7	24	of	of	ADP
fb494745m0v	7	25	characteristic	characteristic	ADJ
fb494745m0v	7	26	p	p	PROPN
fb494745m0v	7	27	&	&	CCONJ
fb494745m0v	7	28	gt	gt	PROPN
fb494745m0v	7	29	;	;	PUNCT
fb494745m0v	7	30	0	0	NUM
fb494745m0v	7	31	.	.	PUNCT
fb494745m0v	8	1	when	when	SCONJ
fb494745m0v	8	2	n=3	n=3	NOUN
fb494745m0v	8	3	,	,	PUNCT
fb494745m0v	8	4	this	this	PRON
fb494745m0v	8	5	is	be	AUX
fb494745m0v	8	6	the	the	DET
fb494745m0v	8	7	result	result	NOUN
fb494745m0v	8	8	of	of	ADP
fb494745m0v	8	9	griffith	griffith	PROPN
fb494745m0v	8	10	from	from	ADP
fb494745m0v	8	11	the	the	DET
fb494745m0v	8	12	70s	70	NOUN
fb494745m0v	8	13	.	.	PUNCT
fb494745m0v	9	1	our	our	PRON
fb494745m0v	9	2	strategy	strategy	NOUN
fb494745m0v	9	3	is	be	AUX
fb494745m0v	9	4	to	to	PART
fb494745m0v	9	5	recast	recast	VERB
fb494745m0v	9	6	the	the	DET
fb494745m0v	9	7	problem	problem	NOUN
fb494745m0v	9	8	in	in	ADP
fb494745m0v	9	9	terms	term	NOUN
fb494745m0v	9	10	of	of	ADP
fb494745m0v	9	11	computing	compute	VERB
fb494745m0v	9	12	cohomology	cohomology	NOUN
fb494745m0v	9	13	of	of	ADP
fb494745m0v	9	14	(	(	PUNCT
fb494745m0v	9	15	twisted	twisted	ADJ
fb494745m0v	9	16	)	)	PUNCT
fb494745m0v	9	17	divided	divide	VERB
fb494745m0v	9	18	powers	power	NOUN
fb494745m0v	9	19	of	of	ADP
fb494745m0v	9	20	cotangent	cotangent	ADJ
fb494745m0v	9	21	sheaf	sheaf	NOUN
fb494745m0v	9	22	on	on	ADP
fb494745m0v	9	23	projective	projective	ADJ
fb494745m0v	9	24	space	space	NOUN
fb494745m0v	9	25	.	.	PUNCT
fb494745m0v	10	1	we	we	PRON
fb494745m0v	10	2	study	study	VERB
fb494745m0v	10	3	the	the	DET
fb494745m0v	10	4	vanishing	vanish	VERB
fb494745m0v	10	5	behavior	behavior	NOUN
fb494745m0v	10	6	by	by	ADP
fb494745m0v	10	7	estimation	estimation	NOUN
fb494745m0v	10	8	of	of	ADP
fb494745m0v	10	9	castelnuovo	castelnuovo	PROPN
fb494745m0v	10	10	-	-	PUNCT
fb494745m0v	10	11	mumford	mumford	PROPN
fb494745m0v	10	12	regularity	regularity	NOUN
fb494745m0v	10	13	of	of	ADP
fb494745m0v	10	14	composition	composition	NOUN
fb494745m0v	10	15	factors	factor	NOUN
fb494745m0v	10	16	induced	induce	VERB
fb494745m0v	10	17	by	by	ADP
fb494745m0v	10	18	natural	natural	ADJ
fb494745m0v	10	19	truncation	truncation	NOUN
fb494745m0v	10	20	of	of	ADP
fb494745m0v	10	21	frobenius	frobenius	NOUN
fb494745m0v	10	22	.	.	PUNCT
fb494745m0v	11	1	we	we	PRON
fb494745m0v	11	2	also	also	ADV
fb494745m0v	11	3	investigate	investigate	VERB
fb494745m0v	11	4	the	the	DET
fb494745m0v	11	5	character	character	NOUN
fb494745m0v	11	6	of	of	ADP
fb494745m0v	11	7	cohomology	cohomology	NOUN
fb494745m0v	11	8	groups	group	NOUN
fb494745m0v	11	9	of	of	ADP
fb494745m0v	11	10	line	line	NOUN
fb494745m0v	11	11	bundles	bundle	NOUN
fb494745m0v	11	12	on	on	ADP
fb494745m0v	11	13	the	the	DET
fb494745m0v	11	14	incidence	incidence	NOUN
fb494745m0v	11	15	correspondence	correspondence	NOUN
fb494745m0v	11	16	with	with	ADP
fb494745m0v	11	17	respect	respect	NOUN
fb494745m0v	11	18	to	to	ADP
fb494745m0v	11	19	the	the	DET
fb494745m0v	11	20	natural	natural	ADJ
fb494745m0v	11	21	action	action	NOUN
fb494745m0v	11	22	of	of	ADP
fb494745m0v	11	23	n	n	ADJ
fb494745m0v	11	24	-	-	PUNCT
fb494745m0v	11	25	dimensional	dimensional	ADJ
fb494745m0v	11	26	torus	torus	NOUN
fb494745m0v	11	27	.	.	PUNCT
fb494745m0v	12	1	when	when	SCONJ
fb494745m0v	12	2	n=3	n=3	ADV
fb494745m0v	12	3	,	,	PUNCT
fb494745m0v	12	4	we	we	PRON
fb494745m0v	12	5	give	give	VERB
fb494745m0v	12	6	an	an	DET
fb494745m0v	12	7	explicit	explicit	ADJ
fb494745m0v	12	8	recursion	recursion	NOUN
fb494745m0v	12	9	formula	formula	NOUN
fb494745m0v	12	10	which	which	PRON
fb494745m0v	12	11	recovers	recover	VERB
fb494745m0v	12	12	the	the	DET
fb494745m0v	12	13	result	result	NOUN
fb494745m0v	12	14	of	of	ADP
fb494745m0v	12	15	linyuan	linyuan	PROPN
fb494745m0v	12	16	liu	liu	PROPN
fb494745m0v	12	17	.	.	PUNCT
fb494745m0v	13	1	we	we	PRON
fb494745m0v	13	2	also	also	ADV
fb494745m0v	13	3	provide	provide	VERB
fb494745m0v	13	4	a	a	DET
fb494745m0v	13	5	resursive	resursive	ADJ
fb494745m0v	13	6	formula	formula	NOUN
fb494745m0v	13	7	in	in	ADP
fb494745m0v	13	8	the	the	DET
fb494745m0v	13	9	case	case	NOUN
fb494745m0v	13	10	n=4	n=4	NOUN
fb494745m0v	13	11	,	,	PUNCT
fb494745m0v	13	12	p=2	p=2	NOUN
fb494745m0v	13	13	.	.	PUNCT
fb494745m0v	14	1	for	for	ADP
fb494745m0v	14	2	the	the	DET
fb494745m0v	14	3	case	case	NOUN
fb494745m0v	14	4	p=2	p=2	SPACE
fb494745m0v	14	5	,	,	PUNCT
fb494745m0v	14	6	we	we	PRON
fb494745m0v	14	7	give	give	VERB
fb494745m0v	14	8	a	a	DET
fb494745m0v	14	9	conjecture	conjecture	NOUN
fb494745m0v	14	10	of	of	ADP
fb494745m0v	14	11	non	non	ADJ
fb494745m0v	14	12	-	-	ADJ
fb494745m0v	14	13	recursive	recursive	ADJ
fb494745m0v	14	14	character	character	NOUN
fb494745m0v	14	15	formula	formula	NOUN
fb494745m0v	14	16	,	,	PUNCT
fb494745m0v	14	17	involving	involve	VERB
fb494745m0v	14	18	symmetric	symmetric	ADJ
fb494745m0v	14	19	polynomials	polynomial	NOUN
fb494745m0v	14	20	naturally	naturally	ADV
fb494745m0v	14	21	defined	define	VERB
fb494745m0v	14	22	in	in	ADP
fb494745m0v	14	23	terms	term	NOUN
fb494745m0v	14	24	of	of	ADP
fb494745m0v	14	25	winning	win	VERB
fb494745m0v	14	26	positions	position	NOUN
fb494745m0v	14	27	of	of	ADP
fb494745m0v	14	28	the	the	DET
fb494745m0v	14	29	game	game	NOUN
fb494745m0v	14	30	of	of	ADP
fb494745m0v	14	31	nim	nim	PROPN
fb494745m0v	14	32	.	.	PUNCT
fb494745m0v	15	1	we	we	PRON
fb494745m0v	15	2	will	will	AUX
fb494745m0v	15	3	show	show	VERB
fb494745m0v	15	4	the	the	DET
fb494745m0v	15	5	conjecture	conjecture	NOUN
fb494745m0v	15	6	holds	hold	VERB
fb494745m0v	15	7	in	in	ADP
fb494745m0v	15	8	the	the	DET
fb494745m0v	15	9	case	case	NOUN
fb494745m0v	15	10	n=3	n=3	PRON
fb494745m0v	15	11	and	and	CCONJ
fb494745m0v	15	12	n=4	n=4	NOUN
fb494745m0v	15	13	.	.	PUNCT