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arXiv · 1307.8356

The inverse deformation problem

Timothy Eardley·Jayanta Manoharmayum
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Abstract

We show the inverse deformation problem has an affirmative answer: given a complete local noetherian ring $A$ with finite residue field $\pmb{k}$, we show that there is a topologically finitely generated profinite group $\Gamma$ and an absolutely irreducible continuous representation $\bar\rho:\Gamma\to GL_n(\pmb{k})$ such that $A$ is the universal deformation ring for $\Gamma,\bar\rho$.

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Timothy Eardley, Jayanta Manoharmayum. 2013-07-31. The inverse deformation problem. https://doi.org/10.1112/s0010437x16007582

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