Journal article
Universal deformation rings need not be complete intersections
Mathematische Annalen, Vol.337(4), pp.739-767
04/2007
DOI: 10.1007/s00208-006-0054-2
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.
Details
- Title: Subtitle
- Universal deformation rings need not be complete intersections
- Creators
- Frauke Bleher - Department of Mathematics University of Iowa Iowa City IA 52242-1419 USATed Chinburg - Department of Mathematics University of Pennsylvania Philadelphia PA 19104-6395 USA
- Resource Type
- Journal article
- Publication Details
- Mathematische Annalen, Vol.337(4), pp.739-767
- DOI
- 10.1007/s00208-006-0054-2
- ISSN
- 0025-5831
- eISSN
- 1432-1807
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- Language
- English
- Date published
- 04/2007
- Academic Unit
- Mathematics
- Record Identifier
- 9983985839802771
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