p-Adic lifting problems and derived equivalences

For two derived equivalent k-algebras and , we introduce a correspondence between O-orders reducing to and O-orders reducing to . We outline how this may be used to transfer properties like uniqueness (or non-existence) of a lift between and . 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 Dκ,0(2A) and Dκ,0(2B) can actually occur as basic algebras of blocks of group rings of finite groups.