Semisimplicity of \'etale cohomology of certain Shimura varieties
Abstract
Building on work of Fayad and Nekov\'ar, 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\'ar with the Eichler-Shimura relations.
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