Admissibility over semi-global fields in the bad characteristic case

TL;DR

This paper characterizes which finite groups are admissible over certain function fields of curves, especially in cases with bad characteristic, extending understanding of Galois groups over these fields.

Contribution

It provides a complete characterization of admissible groups over function fields of curves in the bad characteristic case, filling a gap in the existing theory.

Findings

Complete characterization of admissible groups in the bad characteristic case

Extension of admissibility results to function fields with algebraically closed residue fields

Application to fields like _P((t))(x)

Abstract

A finite group $G$ is said to be admissible over a field $F$ if there exists a division algebra $D$ central over $F$ with a maximal subfield $L$ such that $L/F$ is Galois with group $G$. In this paper we give a complete characterization of admissible groups over function fields of curves over equicharacteristic complete discretely valued fields with algebraically closed residue fields, such as the field $\overline{\mathbb{F}_P}((t))(x)$.