Semisimplicity of étale cohomology of certain Shimura varieties

Abstract

Building on work of Fayad and Nekovář, we show that a certain part of the etale cohomology of some abelian-type Shimura varieties is semisimple, assuming the associated automorphic Galois representations exists, and satisfies some good properties. The proof combines an abstract semisimplicity criterion of Fayad-Nekovář with the Eichler-Shimura relations.

Substantial revision. Main theorem unchanged