p-Adic lifting problems and derived equivalences

For two derived equivalent k-algebras Lambda and Gamma, we introduce a correspondence between O-orders reducing to Lambda and O-orders reducing to Gamma. We outline how this may be used to transfer properties like uniqueness (or non-existence) of a lift between Lambda and Gamma. As an application, we look at tame algebras of dihedral type with two simple modules, where, most notably, we are able to show that among those algebras only the algebras D^{kappa,0}(2A) and D^{kappa,0}(2B) can actually occur as basic algebras of blocks of group rings of finite groups.