1. The local Jacquet–Langlands correspondence and congruences modulo ℓ
- Author
-
Alberto Mínguez, Vincent Sécherre, Institut de Mathématiques de Jussieu (IMJ), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de Versailles (LMV), and Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Mathematics::Number Theory ,General Mathematics ,Modulo ,Congruences mod ,ℓ-adic lifting ,Jacquet–Langlands correspondence ,01 natural sciences ,Jacquet-Langlands correspondence ,Combinatorics ,adic lifting ,Modular representations of p-adic reductive groups ,0103 physical sciences ,Congruence (manifolds) ,0101 mathematics ,Mathematics::Representation Theory ,Local field ,Mathematics ,Cuspidal representations ,[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT] ,010102 general mathematics ,Prime number ,Congruence relation ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Congruences mod ℓ ,Discrete series ,and Phrases: Modular representations of p-adic reductive groups ,Jacquet-Lang- lands correspondence ,Speh representations ,010307 mathematical physics - Abstract
Let F be a non-Archimedean local field of residual characteristic p, and {\ell} be a prime number different from p. We consider the local Jacquet-Langlands correspondence between {\ell}-adic discrete series of GL(n,F) and an inner form GL(m,D). We show that it respects the relationship of congruence modulo {\ell}. More precisely, we show that two integral {\ell}-adic discrete series of GL(m,D) are congruent modulo {\ell} if and only if the same holds for their Jacquet-Langlands transfers to GL(m,D).
- Published
- 2015