The inverse deformation problem
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 $Γ$ and an absolutely irreducible continuous representation $\barρ:Γ\to GL_n(\pmb{k})$ such that $A$ is the universal deformation ring for $Γ,\barρ$.
math.RA↗