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IHARA LEMMA AND LEVEL RAISING IN HIGHER DIMENSION

Part of: Arithmetic algebraic geometry Representation theory of groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  25 January 2021

Pascal Boyer Open the ORCID record for Pascal Boyer [Opens in a new window]
Pascal Boyer*
Affiliation:
Université Sorbonne Paris Nord, LAGA, CNRS, UMR 7539, F-93430, Villetaneuse, France, CoLoss AAPG2019 ([email protected])
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Abstract

A key ingredient in the Taylor–Wiles proof of Fermat’s last theorem is the classical Ihara lemma, which is used to raise the modularity property between some congruent Galois representations. In their work on Sato and Tate, Clozel, Harris and Taylor proposed a generalisation of the Ihara lemma in higher dimension for some similitude groups. The main aim of this paper is to prove some new instances of this generalised Ihara lemma by considering some particular non-pseudo-Eisenstein maximal ideals of unramified Hecke algebras. As a consequence, we prove a level-raising statement.

Keywords

Shimura varietiestorsion in the cohomologymaximal ideal of the Hecke algebralocalised cohomologyGalois representation

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties 11F70: Representation-theoretic methods; automorphic representations over local and global fields 11F80: Galois representations
Secondary: 20C08: Hecke algebras and their representations 11F85: $p$-adic theory, local fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 21 , Issue 5 , September 2022 , pp. 1701 - 1726
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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