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ON THE COHOMOLOGY OF SOME SIMPLE SHIMURA VARIETIES WITH BAD REDUCTION

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  06 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 quaternionic and related unitary Shimura varieties at ramified places. The main results generalize the previous works of Reimann and Kottwitz in this setting to arbitrary levels at $p$, and confirm the expected description of the cohomology due to Langlands and Kottwitz.

Keywords

Shimura varietiesquaternion algebrascohomology

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 18 , Issue 1 , January 2019 , pp. 1 - 24
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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