Patching and admissibility over two-dimensional complete local domains

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 $charE$, 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 $2$.