Deformations and derived equivalences

Bleher, Frauke

doi:10.1090/S0002-9939-06-08269-4

Deformations and derived equivalences
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Proc. Amer. Math. Soc. 134 (2006), 2503-2510 Request permission

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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