Gorenstein singularity categories

The aim of this paper is to introduce Gorenstein singularity category D-gpsg(b) (A), as the Verdier quotient of the Gorenstein derived category D-gp(b) (A) by the triangulated subcategory K-b(GP(A)). The main result shows that, if A is CM-contravariantly finite abelian category, then the Gorenstein singularity category D-gpsg(b) (A) is triangle-equivalent to the Gorenstein defect category D-defect(b) (A) 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. (C) 2015 Elsevier Inc. All rights reserved.