Admissibility of groups over function fields of p-adic curves

Let KK be a field and GG a finite group. The question of ‘admissibility’ of GG over KK was originally posed by Schacher, who gave partial results in the case K=QK=Q. In this paper, we give necessary conditions for admissibility of a finite group GG 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)Qp(t). We also prove a certain Hasse principle for division algebras over such fields.