Singularity categories of derived categories of hereditary algebras are derived categories

摘要

We show that for the path algebra A of an acyclic quiver, the singularity category of the derived category D-b(modA) is triangle equivalent to the derived category of the functor category of mod A, that is, D-sg (D-b(modA)) similar or equal to 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. (C) 2019 Elsevier B.V. All rights reserved.