Patching and admissibility over two-dimensional complete local domains

Neftin, Danny; Paran, Elad

doi:10.2140/ant.2010.4.743

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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

DOI: 10.2140/ant.2010.4.743

Correction: 10.2140/ant.2011.5.287

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 $char E$ , 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

Correction: 27 August 2011

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/

Vol. 4, No. 6, 2010