Correspondance de Jacquet-Langlands locale et congruences modulo ℓ

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 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).
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https://hal.archives-ouvertes.fr/hal-01176189
Contributor : Vincent Sécherre <>
Submitted on : Wednesday, July 15, 2015 - 9:34:36 AM
Last modification on : Thursday, April 4, 2019 - 1:30:51 AM
Document(s) archivé(s) le : Friday, October 16, 2015 - 10:12:35 AM

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  • HAL Id : hal-01176189, version 1
  • ARXIV : 1507.04119

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Alberto Mínguez, Vincent Sécherre. Correspondance de Jacquet-Langlands locale et congruences modulo ℓ. 2015. 〈hal-01176189〉

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