We introduce the notion of categorical absorption of singularities: an operation that removes
from the derived category of a singular variety a small admissible subcategory responsible …

For various 2-Calabi-Yau categories $\mathscr {C} $ for which the stack of objects
$\mathfrak {M} $ has a good moduli space $ p\colon\mathfrak {M}\rightarrow\mathcal {M} …

In this paper we investigate homologically finite-dimensional objects in the derived category
of a given small dg-enhanced triangulated category. Using these we define reflexivity, hfd …

The concept of an abelian DG-category, introduced by the first-named author in Positselski
(Exact DG-categories and fully faithful triangulated inclusion functors. arXiv: 2110.08237 …

This work establishes a condition that determines when strong generation in the bounded
derived category of a Noetherian J-2 scheme is preserved by the derived pushforward of a …

We construct an" almost involution" assigning a new DG-category to a given one, and use
this construction in order to recover, say, the abelian category of graded modules over the …

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 …

K-2mu-theory and the singularity category of quotient singularities Page 1 ANNALS OF K-THEORY
A JOURNAL OF THE K-THEORY FOUNDATION msp vol. 6 no. 3 2021 K-theory and the …

Given a resolution of rational singularities $\pi\colon {\tilde {X}}\to X $ over a field of
characteristic zero, we use a Hodge-theoretic argument to prove that the image of the functor …

Let $\pi\colon Y\to X $ denote the canonical resolution of the two dimensional Kleinian
singularity $ X $ of type ADE. In the present paper, we establish isomorphisms between the …