CONGRUENCE PROPERTIES OF ENDO-CLASSES AND THE LOCAL JACQUET-LANGLANDS CORRESPONDENCE (Analytic, geometric and $p$-adic aspects of automorphic forms and $L$-functions)

Abstract

These are notes from a lecture I gave at RIMS, Kyoto, for the conference Analytic, geometric and p-adic aspects of automorphic forms and L-functions, from 20 to 24 January, 2020. I wish to thank the organizers of this conference. These notes are intended to be a survey of recent results that have been published in [V. Sécherre and S. Stevens, Towards an explicit local Jacquet-Langlands correspondence beyond the cuspidal case, Compositio Math. 155 (2019), 1853-1887.].