p-adic Jacquet-Langlands correspondence and patching

TL;DR

This paper proposes two potential local p-adic Jacquet-Langlands correspondences, demonstrates their isomorphism via patching techniques, and investigates their locally algebraic vectors.

Contribution

It introduces two candidate correspondences and proves their equivalence using patching, advancing understanding of p-adic Jacquet-Langlands theory.

Findings

Two candidate correspondences are shown to be isomorphic.

Analysis of locally algebraic vectors within the correspondence.

Application of patching techniques to establish isomorphism.

Abstract

We describe two candidates for a local p-adic Jacquet-Langlands correspondence and using patching we show that they are in fact isomorphic. We then study locally algebraic vectors of the given correspondence.