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THE $\ell$-MODULAR LOCAL LANGLANDS CORRESPONDENCE AND LOCAL CONSTANTS

Part of: Lie groups Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  08 November 2019

R. Kurinczuk Open the ORCID record for R. Kurinczuk [Opens in a new window]  and
N. Matringe
R. Kurinczuk
Affiliation:
Department of Mathematics, Imperial College London, SW7 2AZ, UK (robkurinczuk@gmail.com)
N. Matringe
Affiliation:
Université de Poitiers, Laboratoire de Mathématiques et Applications, Téléport 2 - BP 30179, Boulevard Marie et Pierre Curie, 86962, Futuroscope Chasseneuil Cedex, France (Nadir.Matringe@math.univ-poitiers.fr)
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Abstract

Let $F$ be a non-archimedean local field of residual characteristic $p$, $\ell \neq p$ be a prime number, and $\text{W}_{F}$ the Weil group of $F$. We classify equivalence classes of $\text{W}_{F}$-semisimple Deligne $\ell$-modular representations of $\text{W}_{F}$ in terms of irreducible $\ell$-modular representations of $\text{W}_{F}$, and extend constructions of Artin–Deligne local constants to this setting. Finally, we define a variant of the $\ell$-modular local Langlands correspondence which satisfies a preservation of local constants statement for pairs of generic representations.

Keywords

modular local Langlands correspondenceDeligne representationslocal constants

MSC classification

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields 11F70: Representation-theoretic methods; automorphic representations over local and global fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 5 , September 2021 , pp. 1585 - 1635
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Copyright
© Cambridge University Press 2019

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