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 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 give a result of Auslander-Ringel-Tachikawa type for Gorenstein-projective modules
over a complete Gorenstein order. In particular, we prove that a complete Gorenstein order …

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 give sufficient conditions for a Frobenius category to be equivalent to the category of
Gorenstein projective modules over an Iwanaga–Gorenstein ring. We then apply this result …

We show the existence of a full exceptional collection in the graded stable derived category
of a Gorenstein isolated quotient singularity using a result of Orlov (2009)[Orl09]. We also …

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 …

The stable derived category D sg (R) of a Gorenstein ring R is defined as the Verdier
quotient of the bounded derived category D b (mod R) by the thick subcategory of perfect …

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 …

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 …