We investigate the behavior of singularity categories and stable categories of Gorenstein
projective modules along a morphism of rings. The natural context to approach the problem …

We study singularity categories through Gorenstein objects in triangulated categories and
silting theory. Let ω be a presilting subcategory of a triangulated category T. We introduce …

Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

We introduce the notion of relative singularity category with respect to any self-orthogonal
subcategory $\omega $ of an abelian category. We introduce the Frobenius category of …

We consider the homotopy category of complexes of projective modules over a Noetherian
ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

We construct a non-affine analogue of the singularity category of a Gorenstein local ring.
With this, Buchweitz's classic equivalence of three triangulated categories over a Gorenstein …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …

New homotopy invariant finiteness conditions on modules over commutative rings are
introduced, and their properties are studied systematically. A number of finiteness results for …

For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …