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Vanishing theorems for the mod p cohomology of some simple Shimura varieties

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  03 November 2020

Teruhisa Koshikawa
Teruhisa Koshikawa*
Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto606-8502, Japan; E-mail: [email protected]

Abstract

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We show that the mod p cohomology of a simple Shimura variety treated in Harris-Taylor’s book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing outside the middle degree under a mild additional assumption.

Keywords

Hecke algebrasGalois representationsShimura varieties

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 11F33: Congruences for modular and $p$-adic modular forms 11F80: Galois representations
Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e38
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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