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Automorphic vector bundles on the stack of G-zips

Part of: Arithmetic problems. Diophantine geometry Linear algebraic groups and related topics

Published online by Cambridge University Press:  03 May 2021

Naoki Imai  and
Jean-Stefan Koskivirta
Naoki Imai
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan; E-mail: naoki@ms.u-tokyo.ac.jp.
Jean-Stefan Koskivirta
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570, Japan; E-mail: jeanstefan.koskivirta@gmail.com.

Abstract

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For a connected reductive group G over a finite field, we study automorphic vector bundles on the stack of G-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the Brylinski-Kostant filtration. Moreover, we give an equivalence of categories between the category of automorphic vector bundles on the stack of G-zips and a category of admissible modules with actions of a 0-dimensional algebraic subgroup a Levi subgroup and monodromy operators.

MSC classification

Primary: 14G35: Modular and Shimura varieties
Secondary: 20G40: Linear algebraic groups over finite fields
Type
Number Theory
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e37
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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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