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Correspondance de Jacquet-Langlands locale et congruences modulo l


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Opened Access Correspondance de Jacquet-Langlands locale et congruences modulo l

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Author: Mínguez Espallargas, Alberto
Sécherre, Vincent
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2017-05
Published in: Inventiones mathematicae, 208 (2), 553-631.
Document type: Article
Abstract: Let F be a non-Archimedean local field of residual characteristic p, and be a prime number different from p. We consider the local Jacquet-Langlands correspondence between -adic discrete series of GLn(F) and an inner form GLm(D). We show that it respects the relationship of congruence modulo . More precisely, we show that two integral -adic discrete series of GLn(F) are congruent modulo if and only if the same holds for their Jacquet- Langlands transfers to GLm(D). We also prove that the Langlands-Jacquet morphism from the Grothendieck group of finite length -adic representations of GLn(F) to that of GLm(D) defined by Badulescu is compatible with reduction mod l.
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DOI: 10.1007/s00222-016-0696-y

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