The aim of this paper is to construct the derived nonhomogeneous Koszul duality. We
consider the derived categories of DG-modules, DG-comodules, and DG-contramodules, the …

We define the triangulated category of relative singularities of a closed subscheme in a
scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations …

To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …

A locally coherent exact category is a finitely accessible additive category endowed with an
exact structure in which the admissible short exact sequences are the directed colimits of the …

Contraherent cosheaves are globalizations of cotorsion (or similar) modules over
commutative rings obtained by gluing together over a scheme. The category of contraherent …

We introduce a new construction of exceptional objects in the derived category of coherent
sheaves on a compact homogeneous space of a semisimple algebraic group and show that …

Let p be a prime number, F a field containing a root of unity of order p, and GF the absolute
Galois group. Extending results of Hopkins, Wickelgren, Minác and Tân, we prove that the …

We extend results of Br\" ustle-Yang on ideal quotients of 2-term subcategories of perfect
derived categories of non-positive dg algebras to a relative setting. We find a new …

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 …

The main goal of this paper is to define the Chow weight structure w Chow for the category
DM c (S) of (constructible) Beilinson motives over any excellent separated finite-dimensional …