Deformations and derived equivalences

Abstract

Suppose A A and B B are block algebras of finite groups over a complete local commutative Noetherian ring whose residue field is a field k 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 A , resp. B B , preserves the versal deformation rings of bounded complexes of finitely generated modules over k A kA , resp. k B kB .