Equations differentielles p-adiques et modules de Jacquet analytiques

TL;DR

This paper employs differential methods to compute Jacquet modules of locally analytic vectors in certain representations of GL_2 over p-adic fields, providing new proofs of existing results and conjectures.

Contribution

It introduces a differential approach to compute Jacquet modules, offering a direct proof of Colmez's results and confirming conjectures by Berger, Breuil, and Emerton.

Findings

Computed Jacquet modules using differential techniques

Provided a direct proof of Colmez's results

Confirmed conjectures by Berger, Breuil, and Emerton

Abstract

Using differential techniques, we compute the Jacquet module of the locally analytic vectors of irreducible admissible unitary representations of GL_2(\qp). This gives a direct proof of some results of Colmez, leading to a proof of conjectures by Berger, Breuil and Emerton.