Abstract
We answer a question of M. Flach by showing that there is a linear representation of a profinite group whose (unrestricted) universal deformation ring is not a complete intersection. We show that such examples arise in arithmetic in the following way. There are infinitely many real quadratic fields F for which there is a mod 2 representation of the Galois group of the maximal unramified extension of F whose universal deformation ring is not a complete intersection. Finally, we discuss bounds on the singularities of universal deformation rings of representations of finite groups in terms of the nilpotency of the associated defect groups.
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