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Bleher, Roberto C. Soto, Ted Chinburg","submitted_at":"2016-12-12T14:26:35Z","abstract_excerpt":"Let $k$ be a field of characteristic $p>0$, and let $W$ be a complete discrete valuation ring of characteristic $0$ that has $k$ as its residue field. Suppose $G$ is a finite group and $G^{\\mathrm{ab},p}$ is its maximal abelian $p$-quotient group. We prove that every endo-trivial $kG$-module $V$ has a universal deformation ring that is isomorphic to the group ring $WG^{\\mathrm{ab},p}$. In particular, this gives a positive answer to a question raised by Bleher and Chinburg for all endo-trivial modules. 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