%0 Journal Article
%T Deformation rings which are not local complete intersections
%A Frauke M. Bleher
%A Ted Chinburg
%A Bart de Smit
%J Mathematics
%D 2010
%I arXiv
%X We study the inverse problem for the versal deformation rings $R(\Gamma,V)$ of finite dimensional representations $V$ of a finite group $\Gamma$ over a field $k$ of positive characteristic $p$. This problem is to determine which complete local commutative Noetherian rings with residue field $k$ can arise up to isomorphism as such $R(\Gamma,V)$. We show that for all integers $n \ge 1$ and all complete local commutative Noetherian rings $\mathcal{W}$ with residue field $k$, the ring $\mathcal{W}[[t]]/(p^n t,t^2)$ arises in this way. This ring is not a local complete intersection if $p^n\mathcal{W}\neq\{0\}$, so we obtain an answer to a question of M. Flach in all characteristics.
%U http://arxiv.org/abs/1003.3143v1