Article
Correspondance de Jacquet-Langlands locale et congruences modulo l
Author/s | Mínguez Espallargas, Alberto
Sécherre, Vincent |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2017-05 |
Deposit Date | 2018-01-25 |
Published in |
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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 ... 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. |
Citation | Mínguez Espallargas, A. y Sécherre, V. (2017). Correspondance de Jacquet-Langlands locale et congruences modulo l. Inventiones mathematicae, 208 (2), 553-631. |
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