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 …

arXiv:2403.05097v1 [math.AC] 8 Mar 2024 Page 1 arXiv:2403.05097v1 [math.AC] 8 Mar 2024
EQUIVALENCES OF STABLE CATEGORIES OF GORENSTEIN LOCAL RINGS TONY J …

We study the following generalization of singularity categories. Let X be a quasi-projective
Gorenstein scheme with isolated singularities and A a non-commutative resolution of …

For a commutative Gorenstein Noetherian ring $ R $, we construct an affine scheme $ X $
solely from singularity category $ D_ {sg}(R) $ of $ R $ such that there is a finite surjective …

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 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 …

Let $ R $ be a commutative Noetherian ring such that $ X= Spec R $ is connected. We prove
that the category $ D^ b (coh X) $ contains no proper full triangulated subcategories which …

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 propose a definition of when a triangulated category should be considered a complete
intersection. We show (using work of Avramov and Gulliksen) that for the derived category of …