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arXiv · 1711.07123

$l$-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients

Paul Hamacher·Wansu Kim
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Abstract

Let $(\mathsf{G},\mathsf{X})$ be a Shimura datum of Hodge type. Let $p$ be an odd prime such that $\mathsf{G}_{\mathbb{Q}_p}$ splits after a tamely ramified extension and $p\nmid |π_1(\mathsf{G}^{\rm der})|$. Under some mild additional assumptions that are satisfied if the associated Shimura variety is proper and $\mathsf{G}_{\mathbb{Q}_p}$ is either unramified or residually split, we prove the generalisation of Mantovan's formula for the $l$-adic cohomology of the associated Shimura variety. On the way we derive some new results about the geometry of the Newton stratification of the reduction modulo $p$ of the Kisin-Pappas integral model.

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Paul Hamacher, Wansu Kim. 2019-02-15. $l$-adic étale cohomology of Shimura varieties of Hodge type with non-trivial coefficients. https://arxiv.org/abs/1711.07123

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