De GL(2,F) a Gal_{Q_p}

TL;DR

This paper constructs a functor linking admissible representations of GL(2,F) over a local field to finite length Galois representations, advancing the understanding of the local Langlands correspondence.

Contribution

It introduces a new functor from admissible finitely presented o-representations of GL(2,F) to finite length Galois representations, applicable for any finite extension F of Q_p.

Findings

Establishes a functorial connection between GL(2,F) and Galois representations.

Applicable to any finite extension F of Q_p.

Bridges representation theory and Galois theory in local fields.

Abstract

We construct a functor from the category of admissible finitely presented o-representations of GL(2,F) to the category of finite length o-representations of Gal_{Q_p}, for any finite extension F of Q_p and the ring of integers o of a finite extension L/Q_p.