The inverse problem for universal deformation rings and the special linear group

Dorobisz, Krzysztof

doi:10.1090/tran6644

The inverse problem for universal deformation rings and the special linear group

Author: Krzysztof Dorobisz
Journal: Trans. Amer. Math. Soc. 368 (2016), 8597-8613
MSC (2010): Primary 11G99; Secondary 11F80, 20C20
DOI: https://doi.org/10.1090/tran6644
Published electronically: March 1, 2016
MathSciNet review: 3551582
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Abstract: We present a solution to the inverse problem for universal deformation rings of group representations. Namely, we show that every complete noetherian local commutative ring with a finite residue field can be realized as the universal deformation ring of a continuous linear representation of a profinite group. More specifically, is the universal deformation ring of the natural representation of $\textup {SL}_n(R)$ in $\textup {SL}_n(k)$ , provided that $n\geq 4$ . We also check for which an analogous result is true in case and .

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