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arXiv · 1507.04119

The local Jacquet--Langlands correspondence and congruences modulo {\ell}

Alberto Mínguez·Vincent Sécherre
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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).

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BibTeXRIS

Alberto Mínguez, Vincent Sécherre. 2015-07-15. The local Jacquet--Langlands correspondence and congruences modulo {\ell}. https://doi.org/10.1007/s00222-016-0696-y

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