Deformation rings which are not local complete intersections

Abstract

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 $p^n\mathcal{W}\ne \{0\}$, so we obtain an answer to a question of M. Flach in all characteristics.

16 pages

References in corpus (1)

• Universal deformation rings and dihedral defect groups