QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED

doi:10.1090/jag/674

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	QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED
	Illusie, Luc 1; Zheng, Weizhe2
	2016-04-01
发表期刊	JOURNAL OF ALGEBRAIC GEOMETRY
ISSN	1056-3911
卷号	25 期号:2 页码:289-400
摘要	Let kappa be an algebraically closed field. Let. be a noetherian commutative ring annihilated by an integer invertible in k and let l be a prime number different from the characteristic of kappa. We prove that if X is a separated algebraic space of finite type over k endowed with an action of a k-algebraic group G, the equivariant etale cohomology algebra H([X/G],A), where [X/G] is the quotient stack of X by G, is finitely generated over A. Moreover, for coefficients K epsilon D-c(+) ([ X/G], F-l) endowed with a commutative multiplicative structure, we establish a structure theorem for H([X/G], K), involving fixed points of elementary abelian l-subgroups of G, which is similar to Quillen's theorem in the case K = F-l. One key ingredient in our proof of the structure theorem is an analysis of specialization of points of the quotient stack. We also discuss variants and generalizations for certain Artin stacks.
DOI	10.1090/jag/674
语种	英语
资助项目	China's Recruitment Program of Global Experts ; National Natural Science Foundation of China[11321101] ; Hua Loo-Keng Key Laboratory of Mathematics ; National Center for Mathematics and Interdisciplinary Sciences ; Chinese Academy of Sciences
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000370976100003
出版者	UNIV PRESS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/22112
专题	数学所
通讯作者	Illusie, Luc; Zheng, Weizhe
作者单位	1.Univ Paris Saclay, CNRS, Univ Paris 11, Lab Math Orsay, F-91405 Orsay, France 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Illusie, Luc,Zheng, Weizhe. QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED[J]. JOURNAL OF ALGEBRAIC GEOMETRY,2016,25(2):289-400.
APA	Illusie, Luc,&Zheng, Weizhe.(2016).QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED.JOURNAL OF ALGEBRAIC GEOMETRY,25(2),289-400.
MLA	Illusie, Luc,et al."QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED".JOURNAL OF ALGEBRAIC GEOMETRY 25.2(2016):289-400.