Universal Deformation Rings Need Not Be Complete Intersections

  • FRAUKE M. BLEHER
  • Published 2006

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.

Cite this paper

@inproceedings{BLEHER2006UniversalDR, title={Universal Deformation Rings Need Not Be Complete Intersections}, author={FRAUKE M. BLEHER}, year={2006} }