  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
$\Gamma,\bar\rho$.
