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The inverse deformation problem
Part of
Timothy Eardley, Jayanta Manoharmayum
Journal:

Compositio Mathematica / Volume 152 / Issue 8 / August 2016

Published online by Cambridge University Press:

14 July 2016, pp. 1725-1739

Print publication:

August 2016
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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 $\unicode[STIX]{x1D6E4},\overline{\unicode[STIX]{x1D70C}}$.