7 citations · 9 across the 14 of their papers we have counts for
14 papers
The contraherent version of the theorem of Slavik and Stovicek
Leonid Positselski
This is a paper about contraherent cosheaves on non-semi-separated schemes. We prove two theorems, a negative one and a positive one. On the negative side, let be a quasi-compa…
Homomorphisms of topological rings and change-of-scalar functors
Leonid Positselski
We consider homomorphisms of complete, separated right or two-sided linear topological rings with countable bases of neighborhoods of zero $\mathfrak f\colon\mathfrak R\to\mathfrak…
Contraherent cosheaves of contramodules on Noetherian formal schemes
Leonid Positselski
There are two main results in this paper: the MGM equivalence between the conventional derived categories of abelian/exact categories, and the derived co-contra correspondence (i.e…
Pseudo-dualizing complexes of torsion modules and semi-infinite MGM duality
Leonid Positselski
This paper is an MGM version of arXiv.org:1703.04266 and arXiv:1907.03364, and a follow-up to Section 5 of arXiv:1503.05523. In the setting of a commutative ring with a weakly…
Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity
Leonid Positselski
Given a hereditary complete cotorsion pair generated by a set of objects in a Grothendieck category , we construct a natural equivalence between…
A relative version of Bass' theorem about finite-dimensional algebras
Leonid Positselski
As a special case of Bass' theory of perfect rings, one obtains the assertion that, over a finite-dimensional associative algebra over a field, all flat modules are projective. In…
Torsion modules and differential operators in infinitely many variables
Leonid Positselski
This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted…
- duality on the contra side
Leonid Positselski
Given a smooth morphism of schemes , denote by the sheaf of rings of fiberwise crystalline differential operators on relative t…
Compact generators of the contraderived category of contramodules
Leonid Positselski, Jan Stovicek
We consider the contraderived category of left contramodules over a right linear topological ring with a countable base of neighborhoods of zero. Equivalently, this i…
A contramodule generalization of Neeman's flat and projective module theorem
Leonid Positselski
This paper builds on top of arXiv:2306.02734. We consider a complete, separated topological ring with a countable base of neighborhoods of zero consisting of open two…
Roos axiom holds for quasi-coherent sheaves
Leonid Positselski
Let be either a quasi-compact semi-separated scheme, or a Noetherian scheme of finite Krull dimension. We show that the Grothendieck abelian category of qua…
Philosophy of contraherent cosheaves
Leonid Positselski
Contraherent cosheaves are module objects over algebraic varieties defined by gluing using the colocalization functors. Contraherent cosheaves are designed to be used for globalizi…
Semialgebras associated with nonunital algebras and -linear subcategories
Leonid Positselski
This paper is a sequel to arXiv:2307.13358 and arXiv:2308.16090. A construction associating a semialgebra with an algebra, subalgebra, and a coalgebra dual to the subalgebra played…
Relative nonhomogeneous Koszul duality
Leonid Positselski
This book contains a detailed exposition of the nonhomogeneous Koszul duality theory in the relative situation over a noncentral, noncommutative, nonsemisimple base ring, as announ…