Inverse problems for deformation rings
Authors:
Frauke M. Bleher, Ted Chinburg and Bart de Smit
Journal:
Trans. Amer. Math. Soc. 365 (2013), 6149-6165
MSC (2010):
Primary 11F80; Secondary 11R32, 20C20
DOI:
https://doi.org/10.1090/S0002-9947-2013-05848-5
Published electronically:
May 14, 2013
MathSciNet review:
3091278
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a complete Noetherian local commutative ring with residue field
of positive characteristic
. We study the inverse problem for the universal deformation rings
relative to
of finite dimensional representations
of a profinite group
over
. We show that for all
and
, the ring
arises as a universal deformation ring. This ring is not a complete intersection if
, so we obtain an answer to a question of M. Flach in all characteristics. We also study the `inverse inverse problem' for the ring
; this is to determine all pairs
such that
is isomorphic to this ring.
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Additional Information
Frauke M. Bleher
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
Email:
frauke-bleher@uiowa.edu
Ted Chinburg
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6395
Email:
ted@math.upenn.edu
Bart de Smit
Affiliation:
Mathematisch Instituut, University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands
Email:
desmit@math.leidenuniv.nl
DOI:
https://doi.org/10.1090/S0002-9947-2013-05848-5
Keywords:
Universal deformation rings,
complete intersections,
inverse problems
Received by editor(s):
February 24, 2012
Received by editor(s) in revised form:
April 5, 2012
Published electronically:
May 14, 2013
Additional Notes:
The first author was supported in part by NSF Grant DMS0651332 and NSA Grant H98230-11-1-0131. The second author was supported in part by NSF Grants DMS0801030 and DMS1100355. The third author was funded in part by the European Commission under contract MRTN-CT-2006-035495.
Article copyright:
© Copyright 2013
Frauke M. Bleher, Ted Chinburg, and Bart de Smit