The inverse deformation problem

Abstract

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

10 pages; statements corrected to exclude the case when the residual representation is $SL_3(\F_2)$

References in corpus (1)

• Inverse Problems for deformation rings

Cited by in corpus (1)

• Deformation rings and images of Galois representations