131 citations · 953 across the 64 of their papers we have counts for
67 papers
Contraderived categories of CDG-modules
Leonid Positselski, Jan Stovicek
For any CDG-ring , we show that the homotopy category of graded-projective (left) CDG-modules over is equivalent to the quotient category of the ho…
Tensor-Hom formalism for modules over nonunital rings
Leonid Positselski
We say that a ring is t-unital if the natural map is an isomorphism, and a left -module is c-unital if the natural map $P\rightarrow\operatorn…
Comodules and contramodules over coalgebras associated with locally finite categories
Leonid Positselski
We explain how to attach a coalgebra over a field to a small -linear category satisfying suitable finiteness conditions. In this context, we study f…
Flat comodules and contramodules as directed colimits, and cotorsion periodicity
Leonid Positselski
This paper is a follow-up to arXiv:2212.09639. We consider two algebraic settings of comodules over a coring and contramodules over a topological ring with a countable base of two-…
A bounded below, noncontractible, acyclic complex of projective modules
Leonid Positselski
We construct examples of bounded below, noncontractible, acyclic complexes of finitely generated projective modules over some rings , as well as bounded above, noncontractible,…
Homological full-and-faithfulness of comodule inclusion and contramodule forgetful functors
Leonid Positselski
In this paper we consider a conilpotent coalgebra over a field . Let be the natural functor of inclusion of the ca…
Generalized periodicity theorems
Leonid Positselski
Let be a ring and be a class of strongly finitely presented (FP) -modules closed under extensions, direct summands, and syzygies. Let $(\mathsf A,\mat…
Local, colocal, and antilocal properties of modules and complexes over commutative rings
Leonid Positselski
This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocal…
Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity
Leonid Positselski, Jan Stovicek
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 gene…
Fp-projective periodicity
Silvana Bazzoni, Michal Hrbek, Leonid Positselski
The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the behavior of the objects of cocycles in acyclic complexes. It is known that any flat $\mathsf{Proj…
Coderived and contraderived categories of locally presentable abelian DG-categories
Leonid Positselski, Jan Stovicek
The concept of an abelian DG-category, introduced by the first-named author in arXiv:2110.08237, unites the notions of abelian categories and (curved) DG-modules in a common framew…
Differential graded Koszul duality: an introductory survey
Leonid Positselski
This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based on the author's memoir arXiv:0905.2621. The paper is intended to serve as a pedagogical intr…
Topologically semiperfect topological rings
Leonid Positselski, Jan Stovicek
We define topologically semiperfect (complete, separated, right linear) topological rings and characterize them by equivalent conditions. We show that the endomorphism ring of a mo…
Closure properties of
Leonid Positselski, Pavel Prihoda, Jan Trlifaj
Let be a class of modules and the class of all direct limits of modules from . The class is well understo…
Exact DG-categories and fully faithful triangulated inclusion functors
Leonid Positselski
We construct an "almost involution" assigning a new DG-category to a given one, and use this construction to recover, say, the abelian category of graded modules over the graded ri…
Quasi-coherent torsion sheaves, the semiderived category, and the semitensor product: Semi-infinite algebraic geometry of quasi-coherent sheaves on ind-schemes
Leonid Positselski
We construct the semi-infinite tensor structure on the semiderived category of quasi-coherent torsion sheaves on an ind-scheme endowed with a flat affine morphism into an ind-Noeth…
Derived, coderived, and contraderived categories of locally presentable abelian categories
Leonid Positselski, Jan Stovicek
For a locally presentable abelian category with a projective generator, we construct the projective derived and contraderived model structures on the category of comple…
Exact categories of topological vector spaces with linear topology
Leonid Positselski
We explain why the naive definition of a natural exact category structure on complete, separated topological vector spaces with linear topology fails. In particular, contrary to ar…
Flat commutative ring epimorphisms of almost Krull dimension zero
Leonid Positselski
We consider flat epimorphisms of commutative rings such that, for every ideal for which , the quotient ring is semilocal of Krull dimension zero.…
An explicit self-dual construction of complete cotorsion pairs in the relative context
Leonid Positselski
Let be a homomorphism of associative rings, and let be a hereditary complete cotorsion pair in . Let $(\mathcal F_A,\mathcal C_A)…
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
Leonid Positselski, Olaf M. Schnürer
Consider the obvious functor from the unbounded derived category of all finitely generated modules over a left noetherian ring to the unbounded derived category of all modules.…
Remarks on derived complete modules and complexes
Leonid Positselski
Let be a commutative ring and a finitely generated ideal. We discuss two definitions of derived -adically complete (also derived -torsion) complexes of -m…
Cofibrant generation of pure monomorphisms
Michael Lieberman, Leonid Positselski, Jiri Rosicky +1
We show that pure monomorphisms are cofibrantly generated---generated from a set of morphisms by pushouts, transfinite composition, and retracts---in any locally finitely presentab…
Projective covers of flat contramodules
Silvana Bazzoni, Leonid Positselski, Jan Stovicek
We show that a direct limit of projective contramodules (over a right linear topological ring) is projective if it has a projective cover. A similar result is obtained for …