Admissibility of groups over function fields of p-adic curves

Abstract

Let K be a field and G a finite group. The question of ‘admissibility’ of G over K was originally posed by Schacher, who gave partial results in the case K=Q. In this paper, we give necessary conditions for admissibility of a finite group G over function fields of curves over complete discretely valued fields. Using this criterion, we give an example of a finite group which is not admissible over Qp(t). We also prove a certain Hasse principle for division algebras over such fields.