Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic $p$

Alexandru Ioan Badulescu (1) , Philippe Roche (1, 2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 L2C - Laboratoire Charles Coulomb

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 × .

Domaines: Mathématiques [math]

Alexandru Ioan Badulescu, Philippe Roche. Global Jacquet-Langlands Correspondence for Division Algebras in Characteristic $p$. International Mathematics Research Notices, 2017, 7, pp.2172-2206. ⟨10.1093/imrn/rnw094⟩. ⟨hal-02067734⟩