Gorenstein singularity categories

The aim of this paper is to introduce Gorenstein singularity category Dgpsgb(A), as the Verdier quotient of the Gorenstein derived category Dgpb(A) by the triangulated subcategory Kb(GP(A))Kb(GP(A)). The main result shows that, if AA is CM-contravariantly finite abelian category, then the Gorenstein singularity category Dgpsgb(A) is triangle-equivalent to the Gorenstein defect category Ddefectb(A) in the sense of [7]. We point out several classes of algebras with non-zero singularity categories, but their Gorenstein singularity categories become zero. We also prove that a Gorenstein derived equivalence between CM-contravariantly finite abelian categories with infinite direct sums induces a Gorenstein singular equivalence.