On the modified mod p local Langlands correspondence for GL_2(Q_{\ell})

TL;DR

This paper provides an explicit description of the modified mod p local Langlands correspondence for GL_2(Q_{ ext{ell}}), enhancing understanding of the relationship between Galois representations and automorphic forms in this setting.

Contribution

It offers a detailed, explicit formulation of the modified mod p local Langlands correspondence for GL_2(Q_{ ext{ell}}), building on the work of Emerton-Helm.

Findings

Explicit description of the modified mod p local Langlands correspondence

Clarification of the correspondence's structure for GL_2(Q_{ell})

Extension of previous theoretical frameworks

Abstract

We give an explicit description of the modified mod p local Langlands correspondence for GL_2(Q_{\ell}) of Emerton-Helm, where p is an odd prime different from \ell.