Global Jacquet-Langlands correspondence for division algebras in characteristic p

Autor:	Badulescu, A. I., Roche, Ph.
Rok vydání:	2013
Předmět:	Mathematics - Number Theory Mathematics - Representation Theory 11F70
Druh dokumentu:	Working Paper
Popis:	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. Comment: 29 pages. We have added references, corrected misprints and corrected a proof
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1302.5289 Zobrazit plný text záznamu View this record from Arxiv