Utilizing previously established results concerning costratification in relative tensor-
triangular geometry, we classify the colocalizing subcategories of the singularity category of …

We develop the theory of costratification in the setting of relative tensor-triangular geometry,
in the sense of Stevenson, providing a unified approach to classification results of Neeman …

We obtain, via the formalism of tensor actions, a complete classification of the localizing
subcategories of the stable derived category of any affine scheme that has hypersurface …

We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …

The singularity category of a ring/scheme is a triangulated category defined to capture the
singularities of the ring/scheme. In the case of a hypersurface $ R/f $, it is given by the …

This work presents a range of triangulated characterizations for important classes of
singularities such as derived splinters, rational singularities, and Du Bois singularities. We …

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 …

In this paper we study derived categories of nodal singularities. We show that for all nodal
singularities there is a categorical resolution whose kernel is generated by a 2 or 3-spherical …

We systematically develop a theory of stratification in the context of tensor triangular
geometry and apply it to classify the localizing tensor-ideals of certain categories of spectral …

A theorem of Orlov from 2004 states that the homotopy category of matrix factorizations on
an affine hypersurface $ Y $ is equivalent to a quotient of the bounded derived category of …