Vol. 4, No. 6, 2010

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Patching and admissibility over two-dimensional complete local domains

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

We develop a patching machinery over the field $E=K\left(\left(X,Y\right)\right)$ 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 $char\phantom{\rule{0.3em}{0ex}}E$, 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
Primary: 12E30
Secondary: 16S35