Locally analytic $\rm{Ext}^1$ for $\rm{GL}_2(\mathbb{Q}_p)$ in de Rham non trianguline case

TL;DR

This paper proves Breuil's conjecture regarding the structure of locally analytic Ext^1 groups for GL_2(Q_p) in the de Rham non-trianguline case, advancing understanding in p-adic representation theory.

Contribution

It establishes the conjecture for a specific class of p-adic representations, providing new insights into the Ext^1 groups in this context.

Findings

Proof of Breuil's conjecture in the non-trianguline case

Enhanced understanding of locally analytic Ext^1 for GL_2(Q_p)

Progress in p-adic representation theory

Abstract

We prove Breuil's conjecture on locally analytic $\rm{Ext}^1$ for $\rm{GL}_2(\mathbb{Q}_p)$ in de Rham non-trianguline case.