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 …

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 …

In this paper, we prove that the bounded derived category Db coh (Y) of coherent sheaves
on a separated scheme Y of finite type over a field k of characteristic zero is homotopically …

We define and study the derived categories of the first kind for curved DG and A-infinity
algebras complete over a pro-Artinian local ring with the curvature elements divisible by the …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

Contramodules are module-like algebraic structures endowed with infinite summation (or,
occasionally, integration) operations satisfying natural axioms. Introduced originally by …

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 …

This paper is a sequel to [L. Positselski, Dedualizing complexes and MGM duality, J. Pure
Appl. Algebra 220 (12)(2016) 3866–3909, arXiv: 1503.05523 [math. CT]; Contraadjusted …