Global Jacquet-Langlands correspondence for division algebras in characteristic p

Abstract : We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero characteristic, we prove that there exists an injective map from the set of automorphic square integrable representations of the multiplicative group of $D$ to the set of automorphic square integrable representations of GL_n(F), compatible at all places with the local Jacquet-Langlands correspondence for unitary representations. We characterize the image of the map. As a consequence we get multiplicity one and strong multiplicity one theorems for the multiplicative group of D.
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International Mathematics Research Notices, Oxford University Press (OUP), 2017, Volume 2017, Issue 7, 1 April 2017, Pages 2172-2206,. 〈10.1093/imrn/rnw094〉
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Soumis le : vendredi 22 février 2013 - 11:54:00
Dernière modification le : vendredi 29 juin 2018 - 11:26:24

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Ioan Alexandru Badulescu, Philippe Roche. Global Jacquet-Langlands correspondence for division algebras in characteristic p. International Mathematics Research Notices, Oxford University Press (OUP), 2017, Volume 2017, Issue 7, 1 April 2017, Pages 2172-2206,. 〈10.1093/imrn/rnw094〉. 〈hal-00793402〉

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