ELEMENTARY ABELIAN l-GROUPS AND MOD l EQUIVARIANT ETALE COHOMOLOGY ALGEBRAS

摘要

This article is a report on joint work with W. Zheng [8]. We give an overview of the main results and sketch their proofs. They mainly consist in variants and generalizations, in the framework of kale cohomology, of theorems of Quillen [14, 15]. Here is an example: if k is an algebraically closed field and l is a prime number different from the characteristic of k, X a separated k-algebraic space of finite type, equipped with an action of a k-algebraic group G, the equivariant etale cohomology algebra H*([X/G],F-l) is finitely generated and is F-isomorphic to a finite projective limit of algebras of the form H* (A, F-l) for A an l-elementary abeliam subgroup of G fixing a point in X.