Geometric realization of the local Langlands correspondence for representations of conductor three

TL;DR

This paper establishes a geometric realization of the local Langlands correspondence for certain two-dimensional Weil group representations of conductor three using local geometric methods on Lubin-Tate curves.

Contribution

It provides a new purely local geometric proof of the local Langlands correspondence for specific representations, expanding understanding of the correspondence's geometric aspects.

Findings

Realization of the correspondence in Lubin-Tate curve cohomology

Purely local geometric proof provided

Focus on representations of conductor three

Abstract

We prove a realization of the local Langlands correspondence for two-dimensional representations of a Weil group of conductor three in the cohomology of Lubin-Tate curves by a purely local geometric method.