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arXiv · 1910.12160

On the inverse problem for deformations of finite group representations

Marcin Lara
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Abstract

Let $s$ be even and $q=p^s$. We show that the ring $W(\mathbb{F}_{q})[\![X]\!]/(X^2-pX)$ is a quotient of the universal deformation ring of a representation of a finite group. This amounts to giving an example of a finite group and its $\mathbb{F}_q$-representation that lifts to $W(\mathbb{F}_q)$ in two different ways and satisfies certain subtle extra conditions. We achieve this by studying representations of $\mathrm{SL}(2,\mathbb{F}_{p^2})$.

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BibTeXRIS

Marcin Lara. 2019-10-27. On the inverse problem for deformations of finite group representations. https://arxiv.org/abs/1910.12160

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