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

Xu Shen

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

Number Theory 2016-11-15 v3

Authors: Xu Shen

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.

Keywords

Shimura varieties $l$-adic cohomology Galois representations $p$-adic uniformization Drinfeld upper half spaces Langlands-Kottwitz conjecture unitary groups

Cite

@article{arxiv.1411.0244,
  title  = {On the $l$-adic cohomology of some $p$-adically uniformized Shimura varieties},
  author = {Xu Shen},
  journal= {arXiv preprint arXiv:1411.0244},
  year   = {2016}
}

Comments

25 pages, slightly revised version, to appear in Journal of the Institute of Mathematics of Jussieu

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