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.
Type de document :
Pré-publication, Document de travail
L2C:13-024. 29 pages. 2013
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https://hal.archives-ouvertes.fr/hal-00793402
Contributeur : L2c Aigle <>
Soumis le : vendredi 22 février 2013 - 11:54:00
Dernière modification le : jeudi 11 janvier 2018 - 06:23:20

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  • HAL Id : hal-00793402, version 1
  • ARXIV : 1302.5289

Citation

A. I. Badulescu, Philippe Roche. Global Jacquet-Langlands correspondence for division algebras in characteristic p. L2C:13-024. 29 pages. 2013. 〈hal-00793402〉

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