Singularity categories of derived categories of hereditary algebras are derived categories

Abstract

We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category Db(modA) is triangle equivalent to the derived category of the functor category of mod_A, that is, Dsg(Db(modA))≃Db(mod(mod_A)). This extends a result in [14] for the path algebra A of a Dynkin quiver. An important step is to establish a functor category analog of Happel's triangle equivalence for repetitive algebras.