A p-adic Jacquet-Langlands Correspondence

Abstract

In this paper, we construct a candidate p-adic Jacquet-Langlands correspondence. This is a correspondence between unitary continuous admissible representations of GL2(Qp) valued in p-adic Banach spaces, and unitary continuous representations of D× valued in p-adic Banach spaces. Here, D is the quaternion algebra over Qp. The characterizing properties that are shown are a local-global compatibility and a calculation of the locally algebraic vectors.