QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED | |
Illusie, Luc1; Zheng, Weizhe2 | |
2016-04-01 | |
Source Publication | JOURNAL OF ALGEBRAIC GEOMETRY |
ISSN | 1056-3911 |
Volume | 25Issue:2Pages:289-400 |
Abstract | 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 |
Language | 英语 |
Funding Project | 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 Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000370976100003 |
Publisher | UNIV PRESS INC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/22112 |
Collection | 数学所 |
Affiliation | 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 |
Recommended Citation 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. |
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