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arXiv · 2206.07283

Semisimplicity of \'etale cohomology of certain Shimura varieties

Si Ying Lee
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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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Si Ying Lee. 2022-06-15. Semisimplicity of \'etale cohomology of certain Shimura varieties. https://arxiv.org/abs/2206.07283

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