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Quotient stacks and mod $l$ equivariant étale cohomology algebras
Luc Illusie 教授(法国巴黎第十一大学)
2018-01-01 12:13  华东师范大学

曹锡华代数论坛

Abstract

(joint work with W. Zheng) In the early 70's Quillen constructed a theory of mod $l$ equivariant cohomology for actions of compact Lie groups on topological spaces. We develop, in the setting of mod $l$ étale cohomology, an analogue of Quillen's theory for actions of algebraic k-groups G on schemes X separated and of finite type over an algebraically closed field k of characteristic different from l. In particular, we show that the equivariant cohomology algebra H^*_G(X,F_l) is finitely generated over F_l, and is determined, up to a power of Frobenius, by the fixed points on X of elementary abelian l-subgroups of G.