Journal article
Inverse problems for deformation rings
Transactions of the American Mathematical Society, Vol.365(11), pp.6149-6165
11/01/2013
DOI: 10.1090/S0002-9947-2013-05848-5
Abstract
Let W be a complete Noetherian local commutative ring with residue field k of positive characteristic p. We study the inverse problem for the universal deformation rings RW(Γ, V) relative to W of finite dimensional representations V of a profinite group Γ over k. We show that for all p and n ≥ 1, the ring W[[t]]/(pnt, t2) arises as a universal deformation ring. This ring is not a complete intersection if pnW ≠ {0}, so we obtain an answer to a question of M. Flach in all characteristics. We also study the 'inverse inverse problem' for the ring W[[t]]/(pnt, t2); this is to determine all pairs (Γ, V) such that RW(Γ, V) is isomorphic to this ring.
Details
- Title: Subtitle
- Inverse problems for deformation rings
- Creators
- Frauke M. Bleher - University of Iowa, MathematicsTed Chinburg - University of PennsylvaniaBart de Smit - Mathematisch Instituut, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.365(11), pp.6149-6165
- DOI
- 10.1090/S0002-9947-2013-05848-5
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society
- Number of pages
- 17
- Language
- English
- Date published
- 11/01/2013
- Academic Unit
- Mathematics
- Record Identifier
- 9983985861402771
Metrics
27 Record Views