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}
}
  • Y. Kimura
  • Published 15 February 2017
  • Mathematics
  • Journal of Pure and Applied Algebra
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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