suresh.venapally@gmail.com

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.

Full text: dvi.gz 37 k, dvi 98 k, ps.gz 591 k, pdf.gz 168 k, pdf 188 k.

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