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ON THE $\ell$-ADIC COHOMOLOGY OF SOME $p$-ADICALLY UNIFORMIZED SHIMURA VARIETIES

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 December 2016

Xu Shen Open the ORCID record for Xu Shen [Opens in a new window]
Xu Shen*
Affiliation:
Fakultät für Mathematik, Universität Regensburg, Universitaetsstr. 31, 93040 Regensburg, Germany (xu.shen@mathematik.uni-regensburg.de)
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Abstract

We determine the Galois representations inside the $\ell$-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 varietiesp-adic uniformizationℓ-adic cohomology

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 14G35: Modular and Shimura varieties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 17 , Issue 5 , November 2018 , pp. 1197 - 1226
Copyright
© Cambridge University Press 2016 

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Footnotes

†

Current address: Morningside Center of Mathematics, No. 55, Zhongguancun East Road, Beijing 100190, China. E-mail: shen@math.ac.cn

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