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 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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Submitted on : Monday, March 25, 2019 - 4:11:55 PM
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Alexandru Ioan Badulescu, Philippe Roche. Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic $p$. International Mathematics Research Notices, Oxford University Press (OUP), 2017, 7, pp.2172-2206. ⟨10.1093/imrn/rnw094⟩. ⟨hal-02067734⟩

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