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HECKE OPERATORS AND THE COHERENT COHOMOLOGY OF SHIMURA VARIETIES

Part of: Arithmetic algebraic geometry Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 April 2021

Najmuddin Fakhruddin  and
Vincent Pilloni Open the ORCID record for Vincent Pilloni [Opens in a new window]
Najmuddin Fakhruddin
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, INDIA (naf@math.tifr.res.in)
Vincent Pilloni
Affiliation:
CNRS, Ecole Normale Supérieure de Lyon, Lyon, FRANCE (vincent.pilloni@ens-lyon.fr)
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Abstract

We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture describing which Hecke operators should act integrally and solve the conjecture in certain cases. As a consequence, we obtain p-adic estimates of Satake parameters of certain nonregular self-dual automorphic representations of $\mathrm {GL}_n$.

Keywords

automorphic formsShimura varietiesHecke operators

MSC classification

Primary: 11F46: Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms
Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties

Information

Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 1 , January 2023 , pp. 1 - 69
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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