
Given a commutative complete local noetherian ring $A$ with finite residue field $\boldsymbol{k}$, we show that there is a topologically finitely generated profinite group $\unicode[STIX]{x1D6E4}$ and an absolutely irreducible continuous representation $\overline{\unicode[STIX]{x1D70C}}:\unicode[STIX]{x1D6E4}\rightarrow \text{GL}_{n}(\boldsymbol{k})$ such that $A$ is a universal deformation ring for $\unicode[STIX]{x1D6E4},\overline{\unicode[STIX]{x1D70C}}$.
20C20, 20E18, 11F80, Mathematics - Number Theory, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, Number Theory (math.NT)
20C20, 20E18, 11F80, Mathematics - Number Theory, Rings and Algebras (math.RA), FOS: Mathematics, Mathematics - Rings and Algebras, Number Theory (math.NT)
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