We study the relationship between derived categories of factorizations on gauged Landau–
Ginzburg models related by variations of the linearization in Geometric Invariant Theory …

In this paper we prove the smoothness of the moduli space of Landau–Ginzburg models. We
formulate and prove a Bogomolov–Tian–Todorov theorem for the deformations of Landau …

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 …

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based
on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011) …

Given a quiver with potential $(Q, W) $, Kontsevich–Soibelman constructed a cohomological
Hall algebra (CoHA) on the critical cohomology of the stack of representations of $(Q, W) …

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 …

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme
is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More …

We prove a Knörrer-periodicity-type equivalence between derived factorization categories of
gauged Landau–Ginzburg models, which is an analogy of a theorem proved by Shipman …

We develop a version of Hodge theory for a large class of smooth formally proper quotient
stacks X∕ G analogous to Hodge theory for smooth projective schemes. We show that the …

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