Local Galois representations of Swan conductor one

Abstract

We construct the local Galois representations over the complex field whose Swan conductors are one by using etale 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 etale cohomology of Artin-Schreier varieties.

arXiv comment41 pages

References in corpus (9)

• Langlands parameters for epipelagic representations of ${\text{GL}}_n$
• Local Fourier transform and epsilon factors
• Character sums associated to finite Coxeter groups
• Geometric realization of the local Langlands correspondence for representations of conductor three
• Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences
• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations I: tame case
• Stable models of Lubin-Tate curves with level three
• Local Jacquet-Langlands correspondences for simple supercuspidal representations
• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case

Cited by in corpus (8)

• Geometric realization of the local Langlands correspondence for representations of conductor three
• Geometric construction of Heisenberg-Weil representations for finite unitary groups and Howe correspondences
• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations I: tame case
• Affinoids in the Lubin-Tate perfectoid space and simple supercuspidal representations II: wild case
• Simple supercuspidal L-packets of quasi-split classical groups
• Geometric approach to the explicit local Langlands correspondence
• Endoscopic lifting of simple supercuspidal representations of unramified U(N) to GL(N)
• Endoscopic lifting of simple supercuspidal representations of SO(2n+1) to GL(2n)