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1 IMJ - Institut de Mathématiques de Jussieu 2 LMV - Laboratoire de Mathématiques de Versailles

Abstract : Let F be a non-Archimedean local field of residual characteristic p, and ℓ be a prime number different from p. We consider the local Jacquet-Langlands correspondence between ℓ-adic discrete series of GLn,F and an inner form GLm,D. We show that it respects the relationship of congruence modulo ℓ. More precisely, we show that two integral ℓ-adic discrete series of GLm,D are congruent modulo ℓ if and only if the same holds for their Jacquet-Langlands transfers to GLm,D.

Keywords : Congruences mod ℓ Speh representations Jacquet-Langlands correspondence Modular representations of p-adic reductive groups





Autor: Alberto Mínguez - Vincent Sécherre -

Fuente: https://hal.archives-ouvertes.fr/



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