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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Deformations and derived equivalences


Author: Frauke M. Bleher
Journal: Proc. Amer. Math. Soc. 134 (2006), 2503-2510
MSC (2000): Primary 20C05; Secondary 18E30
Published electronically: February 17, 2006
MathSciNet review: 2213727
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Abstract: Suppose $ A$ and $ B$ are block algebras of finite groups over a complete local commutative Noetherian ring whose residue field is a field $ k$ of positive characteristic. We prove that a split-endomorphism two-sided tilting complex (as introduced by Rickard) for the derived categories of bounded complexes of finitely generated modules over $ A$, resp. $ B$, preserves the versal deformation rings of bounded complexes of finitely generated modules over $ kA$, resp. $ kB$.


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Additional Information

Frauke M. Bleher
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242-1419
Email: fbleher@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08269-4
PII: S 0002-9939(06)08269-4
Keywords: Universal deformations, versal deformations, derived categories, derived equivalences, abelian defect group conjecture, tilting complexes
Received by editor(s): May 7, 2004
Received by editor(s) in revised form: March 27, 2005
Published electronically: February 17, 2006
Additional Notes: The author was supported in part by NSA Young Investigator Grant MDA904-01-1-0050 and NSF Grant DMS01-39737.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.