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The Plectic Weight Filtration on Cohomology of Shimura Varieties and Partial Frobenius

Part of: Modules, bimodules and ideals Rings and algebras with additional structure

Published online by Cambridge University Press:  12 April 2021

Zhiyou Wu
Zhiyou Wu*
Affiliation:
Max Planck Institute for Mathematics, Bonn53111, Germany; E-mail: [email protected]

Abstract

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We prove that there is a natural plectic weight filtration on the cohomology of Hilbert modular varieties in the spirit of Nekovář and Scholl. This is achieved with the help of Morel’s work on weight t-structures and a detailed study of partial Frobenius. We prove in particular that the partial Frobenius extends to toroidal and minimal compactifications.

MSC classification

Primary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures
Secondary: 16D50: Injective modules, self-injective rings
Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e30
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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), 2021. Published by Cambridge University Press

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