Relative Singularity Categories

الأصل · EN

We study the properties of the relative derived category DCᵇ(A) of an abelian category A relative to a full and additive subcategory C. In particular, when A=A- for a finite-dimensional algebra A over a field and C is a contravariantly finite subcategory of A- which is admissible and closed under direct summands, the C-singularity category DCsg(A)=DCᵇ(A)/Kᵇ(C) is studied. We give a sufficient condition when this category is triangulated equivalent to the stable category of the Gorenstein category G(C) of C.