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Semisimplicity of étale cohomology of certain Shimura varieties (2206.07283v1)
Published 15 Jun 2022 in math.NT
Abstract: Building on work of Fayad and Nekov\'{a}\v{r}, 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-Nekov\'{a}\v{r} with the Eichler-Shimura relations.
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