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Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic $p$ 
Auteur(s): Badulescu Alexandru Ioan, Roche P.
(Article) Publié:
International Mathematics Research Notices, vol. 7 p.2172–2206 (2017)
Texte intégral en Openaccess : 
Ref HAL: hal-02067734_v1
DOI: 10.1093/imrn/rnw094
WoS: 000404041400007
Exporter : BibTex | endNote
6 Citations
Résumé: 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 representations 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 D × .
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