10 papers
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…
Contraherent cosheaves of contramodules on Noetherian formal schemes
Leonid Positselski
We define the exact category of contraherent cosheaves of contramodules on a locally Noetherian formal scheme, as well as the exact categories of locally contraherent cosheaves of…
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…
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…
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…
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…