A categorical p-adic Langlands correspondence for GL_2(Q_p)

TL;DR

This paper constructs a fully faithful functor linking smooth p-adic representations of GL_2(Q_p) to Ind-coherent sheaves on a stack of (phi,Gamma)-modules, advancing the categorical understanding in p-adic Langlands theory.

Contribution

It introduces a new functor establishing a categorical correspondence between p-adic representations and geometric objects, extending the p-adic Langlands program for GL_2(Q_p).

Findings

Constructs a fully faithful functor between derived categories.

Bridges smooth p-adic representations and geometric sheaves.

Enhances the categorical framework of p-adic Langlands correspondence.

Abstract

Let p at least 5 be prime. We construct a fully faithful functor from the derived category of all smooth p-adic representations of GL_2(Q_p) (with a fixed central character) to a derived category of Ind-coherent sheaves on a stack of (phi,Gamma)-modules.