On the $l$-adic cohomology of some $p$-adically uniformized Shimura varieties

Xu Shen

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arXiv · 1411.0244

On the $l$-adic cohomology of some $p$-adically uniformized Shimura varieties

Xu Shen

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Abstract

We determine the Galois representations inside the $l$-adic cohomology of some unitary Shimura varieties at split places where they admit uniformization by finite products of Drinfeld upper half spaces. Our main results confirm Langlands-Kottwitz's description of the cohomology of Shimura varieties in new cases.

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Xu Shen. 2014-11-02. On the $l$-adic cohomology of some $p$-adically uniformized Shimura varieties. https://arxiv.org/abs/1411.0244

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