id	sid	tid	token	lemma	pos
8s45q814g2m	1	1	the	the	DET
8s45q814g2m	1	2	classical	classical	ADJ
8s45q814g2m	1	3	mahowald	mahowald	NOUN
8s45q814g2m	1	4	invariant	invariant	NOUN
8s45q814g2m	1	5	is	be	AUX
8s45q814g2m	1	6	a	a	DET
8s45q814g2m	1	7	method	method	NOUN
8s45q814g2m	1	8	for	for	ADP
8s45q814g2m	1	9	producing	produce	VERB
8s45q814g2m	1	10	nonzero	nonzero	NOUN
8s45q814g2m	1	11	classes	class	NOUN
8s45q814g2m	1	12	in	in	ADP
8s45q814g2m	1	13	the	the	DET
8s45q814g2m	1	14	stable	stable	ADJ
8s45q814g2m	1	15	homotopy	homotopy	NOUN
8s45q814g2m	1	16	groups	group	NOUN
8s45q814g2m	1	17	of	of	ADP
8s45q814g2m	1	18	spheres	sphere	NOUN
8s45q814g2m	1	19	from	from	ADP
8s45q814g2m	1	20	classes	class	NOUN
8s45q814g2m	1	21	in	in	ADP
8s45q814g2m	1	22	lower	low	ADJ
8s45q814g2m	1	23	stems	stem	NOUN
8s45q814g2m	1	24	.	.	PUNCT
8s45q814g2m	2	1	in	in	ADP
8s45q814g2m	2	2	this	this	DET
8s45q814g2m	2	3	thesis	thesis	NOUN
8s45q814g2m	2	4	,	,	PUNCT
8s45q814g2m	2	5	we	we	PRON
8s45q814g2m	2	6	study	study	VERB
8s45q814g2m	2	7	the	the	DET
8s45q814g2m	2	8	mahowald	mahowald	NOUN
8s45q814g2m	2	9	invariant	invariant	NOUN
8s45q814g2m	2	10	in	in	ADP
8s45q814g2m	2	11	the	the	DET
8s45q814g2m	2	12	settings	setting	NOUN
8s45q814g2m	2	13	of	of	ADP
8s45q814g2m	2	14	motivic	motivic	ADJ
8s45q814g2m	2	15	stable	stable	ADJ
8s45q814g2m	2	16	homotopy	homotopy	NOUN
8s45q814g2m	2	17	theory	theory	NOUN
8s45q814g2m	2	18	over	over	ADP
8s45q814g2m	2	19	spec(c	spec(c	PROPN
8s45q814g2m	2	20	)	)	PUNCT
8s45q814g2m	2	21	and	and	CCONJ
8s45q814g2m	2	22	spec(r	spec(r	PROPN
8s45q814g2m	2	23	)	)	PUNCT
8s45q814g2m	2	24	,	,	PUNCT
8s45q814g2m	2	25	as	as	ADV
8s45q814g2m	2	26	well	well	ADV
8s45q814g2m	2	27	as	as	ADP
8s45q814g2m	2	28	c2	c2	PROPN
8s45q814g2m	2	29	-	-	PUNCT
8s45q814g2m	2	30	equivariant	equivariant	ADJ
8s45q814g2m	2	31	stable	stable	ADJ
8s45q814g2m	2	32	homotopy	homotopy	NOUN
8s45q814g2m	2	33	theory	theory	NOUN
8s45q814g2m	2	34	.	.	PUNCT
8s45q814g2m	3	1	in	in	ADP
8s45q814g2m	3	2	the	the	DET
8s45q814g2m	3	3	c2	c2	PROPN
8s45q814g2m	3	4	-	-	PUNCT
8s45q814g2m	3	5	equivariant	equivariant	ADJ
8s45q814g2m	3	6	setting	setting	NOUN
8s45q814g2m	3	7	,	,	PUNCT
8s45q814g2m	3	8	we	we	PRON
8s45q814g2m	3	9	prove	prove	VERB
8s45q814g2m	3	10	an	an	DET
8s45q814g2m	3	11	analog	analog	NOUN
8s45q814g2m	3	12	of	of	ADP
8s45q814g2m	3	13	lin	lin	PROPN
8s45q814g2m	3	14	's	's	PART
8s45q814g2m	3	15	theorem	theorem	NOUN
8s45q814g2m	3	16	by	by	ADP
8s45q814g2m	3	17	adapting	adapt	VERB
8s45q814g2m	3	18	the	the	DET
8s45q814g2m	3	19	motivic	motivic	ADJ
8s45q814g2m	3	20	singer	singer	NOUN
8s45q814g2m	3	21	construction	construction	NOUN
8s45q814g2m	3	22	developed	develop	VERB
8s45q814g2m	3	23	by	by	ADP
8s45q814g2m	3	24	gregersen	gregersen	PROPN
8s45q814g2m	3	25	to	to	ADP
8s45q814g2m	3	26	the	the	DET
8s45q814g2m	3	27	c2	c2	PROPN
8s45q814g2m	3	28	-	-	PUNCT
8s45q814g2m	3	29	equivariant	equivariant	ADJ
8s45q814g2m	3	30	setting	setting	NOUN
8s45q814g2m	3	31	.	.	PUNCT
8s45q814g2m	4	1	we	we	PRON
8s45q814g2m	4	2	compute	compute	VERB
8s45q814g2m	4	3	a	a	DET
8s45q814g2m	4	4	motivic	motivic	ADJ
8s45q814g2m	4	5	version	version	NOUN
8s45q814g2m	4	6	of	of	ADP
8s45q814g2m	4	7	the	the	DET
8s45q814g2m	4	8	tate	tate	NOUN
8s45q814g2m	4	9	construction	construction	NOUN
8s45q814g2m	4	10	for	for	ADP
8s45q814g2m	4	11	various	various	ADJ
8s45q814g2m	4	12	motivic	motivic	ADJ
8s45q814g2m	4	13	spectra	spectra	NOUN
8s45q814g2m	4	14	,	,	PUNCT
8s45q814g2m	4	15	and	and	CCONJ
8s45q814g2m	4	16	show	show	VERB
8s45q814g2m	4	17	that	that	SCONJ
8s45q814g2m	4	18	this	this	DET
8s45q814g2m	4	19	construction	construction	NOUN
8s45q814g2m	4	20	produces	produce	VERB
8s45q814g2m	4	21	"	"	PUNCT
8s45q814g2m	4	22	blueshift	blueshift	NOUN
8s45q814g2m	4	23	"	"	PUNCT
8s45q814g2m	4	24	in	in	ADP
8s45q814g2m	4	25	these	these	DET
8s45q814g2m	4	26	cases	case	NOUN
8s45q814g2m	4	27	.	.	PUNCT
8s45q814g2m	5	1	in	in	ADP
8s45q814g2m	5	2	the	the	DET
8s45q814g2m	5	3	complex	complex	ADJ
8s45q814g2m	5	4	motivic	motivic	ADJ
8s45q814g2m	5	5	case	case	NOUN
8s45q814g2m	5	6	,	,	PUNCT
8s45q814g2m	5	7	we	we	PRON
8s45q814g2m	5	8	use	use	VERB
8s45q814g2m	5	9	these	these	DET
8s45q814g2m	5	10	computations	computation	NOUN
8s45q814g2m	5	11	to	to	PART
8s45q814g2m	5	12	show	show	VERB
8s45q814g2m	5	13	that	that	SCONJ
8s45q814g2m	5	14	the	the	DET
8s45q814g2m	5	15	mahowald	mahowald	ADJ
8s45q814g2m	5	16	invariant	invariant	NOUN
8s45q814g2m	5	17	of	of	ADP
8s45q814g2m	5	18	η^i	η^i	X
8s45q814g2m	5	19	,	,	PUNCT
8s45q814g2m	5	20	i	i	PRON
8s45q814g2m	5	21	≥	≥	X
8s45q814g2m	5	22	1	1	NUM
8s45q814g2m	5	23	,	,	PUNCT
8s45q814g2m	5	24	is	be	AUX
8s45q814g2m	5	25	the	the	DET
8s45q814g2m	5	26	first	first	ADJ
8s45q814g2m	5	27	element	element	NOUN
8s45q814g2m	5	28	in	in	ADP
8s45q814g2m	5	29	adams	adams	PROPN
8s45q814g2m	5	30	filtration	filtration	PROPN
8s45q814g2m	5	31	i	i	PRON
8s45q814g2m	5	32	of	of	ADP
8s45q814g2m	5	33	the	the	DET
8s45q814g2m	5	34	w1	w1	NOUN
8s45q814g2m	5	35	-	-	PUNCT
8s45q814g2m	5	36	periodic	periodic	ADJ
8s45q814g2m	5	37	families	family	NOUN
8s45q814g2m	5	38	constructed	construct	VERB
8s45q814g2m	5	39	by	by	ADP
8s45q814g2m	5	40	andrews	andrews	PROPN
8s45q814g2m	5	41	.	.	PUNCT
8s45q814g2m	6	1	this	this	PRON
8s45q814g2m	6	2	provides	provide	VERB
8s45q814g2m	6	3	an	an	DET
8s45q814g2m	6	4	exotic	exotic	ADJ
8s45q814g2m	6	5	periodic	periodic	ADJ
8s45q814g2m	6	6	analog	analog	NOUN
8s45q814g2m	6	7	of	of	ADP
8s45q814g2m	6	8	mahowald	mahowald	PROPN
8s45q814g2m	6	9	and	and	CCONJ
8s45q814g2m	6	10	ravenel	ravenel	PROPN
8s45q814g2m	6	11	's	's	PART
8s45q814g2m	6	12	computation	computation	NOUN
8s45q814g2m	6	13	that	that	SCONJ
8s45q814g2m	6	14	the	the	DET
8s45q814g2m	6	15	classical	classical	ADJ
8s45q814g2m	6	16	mahowald	mahowald	NOUN
8s45q814g2m	6	17	invariant	invariant	NOUN
8s45q814g2m	6	18	of	of	ADP
8s45q814g2m	6	19	2^i	2^i	NUM
8s45q814g2m	6	20	,	,	PUNCT
8s45q814g2m	6	21	i	i	PRON
8s45q814g2m	6	22	≥	≥	PROPN
8s45q814g2m	6	23	1	1	NUM
8s45q814g2m	6	24	,	,	PUNCT
8s45q814g2m	6	25	is	be	AUX
8s45q814g2m	6	26	the	the	DET
8s45q814g2m	6	27	first	first	ADJ
8s45q814g2m	6	28	element	element	NOUN
8s45q814g2m	6	29	in	in	ADP
8s45q814g2m	6	30	adams	adams	PROPN
8s45q814g2m	6	31	filtration	filtration	PROPN
8s45q814g2m	6	32	i	i	PRON
8s45q814g2m	6	33	of	of	ADP
8s45q814g2m	6	34	the	the	DET
8s45q814g2m	6	35	v1	v1	ADJ
8s45q814g2m	6	36	-	-	ADJ
8s45q814g2m	6	37	periodic	periodic	ADJ
8s45q814g2m	6	38	families	family	NOUN
8s45q814g2m	6	39	constructed	construct	VERB
8s45q814g2m	6	40	by	by	ADP
8s45q814g2m	6	41	adams	adams	PROPN
8s45q814g2m	6	42	.	.	PUNCT
8s45q814g2m	7	1	we	we	PRON
8s45q814g2m	7	2	obtain	obtain	VERB
8s45q814g2m	7	3	similar	similar	ADJ
8s45q814g2m	7	4	results	result	NOUN
8s45q814g2m	7	5	in	in	ADP
8s45q814g2m	7	6	both	both	CCONJ
8s45q814g2m	7	7	the	the	DET
8s45q814g2m	7	8	real	real	ADJ
8s45q814g2m	7	9	motivic	motivic	PROPN
8s45q814g2m	7	10	and	and	CCONJ
8s45q814g2m	7	11	c2	c2	PROPN
8s45q814g2m	7	12	-	-	PUNCT
8s45q814g2m	7	13	equivariant	equivariant	ADJ
8s45q814g2m	7	14	settings	setting	NOUN
8s45q814g2m	7	15	.	.	PUNCT
8s45q814g2m	8	1	finally	finally	ADV
8s45q814g2m	8	2	,	,	PUNCT
8s45q814g2m	8	3	we	we	PRON
8s45q814g2m	8	4	also	also	ADV
8s45q814g2m	8	5	study	study	VERB
8s45q814g2m	8	6	the	the	DET
8s45q814g2m	8	7	behavior	behavior	NOUN
8s45q814g2m	8	8	of	of	ADP
8s45q814g2m	8	9	the	the	DET
8s45q814g2m	8	10	mahowald	mahowald	ADJ
8s45q814g2m	8	11	invariant	invariant	NOUN
8s45q814g2m	8	12	under	under	ADP
8s45q814g2m	8	13	various	various	ADJ
8s45q814g2m	8	14	functors	functor	NOUN
8s45q814g2m	8	15	between	between	ADP
8s45q814g2m	8	16	the	the	DET
8s45q814g2m	8	17	motivic	motivic	PROPN
8s45q814g2m	8	18	,	,	PUNCT
8s45q814g2m	8	19	equivariant	equivariant	NOUN
8s45q814g2m	8	20	,	,	PUNCT
8s45q814g2m	8	21	and	and	CCONJ
8s45q814g2m	8	22	classical	classical	ADJ
8s45q814g2m	8	23	stable	stable	ADJ
8s45q814g2m	8	24	homotopy	homotopy	NOUN
8s45q814g2m	8	25	categories	category	NOUN
8s45q814g2m	8	26	.	.	PUNCT