  We show that every complete noetherian local commutative ring R with residue
field k can be realized as a universal deformation ring of a continuous linear
representation of a profinite group. More specifically, R is the universal
deformation ring of the natural representation of SL_n(R) in SL_n(k), provided
that n is at least 4. We also check for which R an analogous result is true in
case n=2 and n=3.
