Local Galois representations of Swan conductor one

Naoki Imai and Takahiro Tsushima

Vol. 326 (2023), No. 1, 37–83

DOI: 10.2140/pjm.2023.326.37

Abstract

We construct the local Galois representations over the complex field whose Swan conductors are one by using étale cohomology of Artin–Schreier sheaves on affine lines over finite fields. Then, we study the Galois representations, and give an explicit description of the local Langlands correspondences for simple supercuspidal representations. We discuss also a more natural realization of the Galois representations in the étale cohomology of Artin–Schreier varieties.

Keywords

Galois representation, simple supercuspidal representation, local Langlands correspondence

Mathematical Subject Classification

Primary: 11F80

Secondary: 11F70

Milestones

Received: 14 November 2023

Accepted: 14 November 2023

Published: 14 December 2023