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 D b ( mod A ) is triangle equivalent to the derived category of the functor category of mod _ A , that is, D sg ( D b ( mod A ) ) ≃ D b ( 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.