Vol. 4, No. 6, 2010

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Patching and admissibility over two-dimensional complete local domains

Danny Neftin and Elad Paran

Vol. 4 (2010), No. 6, 743–762
Abstract

We develop a patching machinery over the field E = K((X,Y )) of formal power series in two variables over an infinite field K. We apply this machinery to prove that if K is separably closed and G is a finite group of order not divisible by charE, then there exists a G-crossed product algebra with center E if and only if the Sylow subgroups of G are abelian of rank at most 2.

Keywords
patching, admissible groups, division algebras, complete local domains
Mathematical Subject Classification 2000
Primary: 12E30
Secondary: 16S35
Milestones
Received: 9 October 2009
Revised: 15 February 2010
Accepted: 21 March 2010
Published: 25 September 2010
Authors
Danny Neftin
Department of Mathematics
Technion – Institute of Technology
Haifa 32000
Israel
Elad Paran
Einstein Institute of Mathematics
Edmond J. Safra Campus
Givat Ram
The Hebrew University of Jerusalem
Jerusalem 91904
Israel
http://www.tau.ac.il/~paranela/