# Singularity categories of derived categories of hereditary algebras are derived categories

@article{Kimura2017SingularityCO, title={Singularity categories of derived categories of hereditary algebras are derived categories}, author={Yuta Kimura}, journal={Journal of Pure and Applied Algebra}, year={2017}, volume={224}, pages={836-859} }

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.

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