The local Jacquet–Langlands correspondence and congruences modulo ℓ
Correspondance de Jacquet-Langlands locale et congruences modulo ℓ
Résumé
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 GL(n,F) and an inner form GL(m,D). We show that it respects the relationship of congruence modulo ℓ. More precisely, we show that two integral ℓ-adic discrete series of GL(m,D) are congruent modulo ℓ if and only if the same holds for their Jacquet-Langlands transfers to GL(m,D).
Mots clés
Congruences mod ℓ
Speh representations
Jacquet-Langlands correspondence
Modular representations of p-adic reductive groups
and Phrases: Modular representations of p-adic reductive groups
Jacquet-Lang- lands correspondence
Cuspidal representations
-adic lifting
Congruences mod
Congruences mod ℓ
ℓ-adic lifting
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