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QUOTIENT STACKS AND EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS: QUILLEN'S THEORY REVISITED
Illusie, Luc1; Zheng, Weizhe2
2016-04-01
Source PublicationJOURNAL OF ALGEBRAIC GEOMETRY
ISSN1056-3911
Volume25Issue:2Pages:289-400
AbstractLet 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.
DOI10.1090/jag/674
Language英语
Funding ProjectChina'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 AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000370976100003
PublisherUNIV PRESS INC
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/22112
Collection数学所
Affiliation1.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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