On the geometrization of the $p$-adic local Langlands correspondence

TL;DR

This paper surveys the progress in geometrizing aspects of the $p$-adic local Langlands correspondence for ${ m GL}_2({f Q}_p)$, aiming to deepen understanding through geometric methods.

Contribution

It provides an overview of recent developments in geometrizing the $p$-adic local Langlands correspondence for ${ m GL}_2({f Q}_p)$.

Findings

Summarizes key results in the geometrization approach.

Highlights connections between geometry and $p$-adic Langlands.

Identifies open problems and future directions.

Abstract

We survey results related to our geometrization of a part of the $p$-adic local Langlands correspondence for ${\mathrm{GL}}_2({\mathbf Q}_p)$.