Submission: 2012, Jan 9
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.
2010 Mathematics Subject Classification: 11R52, 12E15, 12F12, 12E30
Keywords and Phrases: Admissible groups, Hasse principle, central simple algebras, function fields of curves over complete discretely valued field.
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