131 citations · 953 across the 64 of their papers we have counts for
7 papers · 1 filter
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 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.…
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…
Countably generated flat modules are quite flat
Michal Hrbek, Leonid Positselski, Alexander Slávik
We prove that if is a commutative Noetherian ring, then every countably generated flat -module is quite flat, i.e., a direct summand of a transfinite extension of localizati…
-almost perfect commutative rings
Silvana Bazzoni, Leonid Positselski
Given a multiplicative subset in a commutative ring , we consider -weakly cotorsion and -strongly flat -modules, and show that all -modules have -strongly fla…
On strongly flat and weakly cotorsion modules
Leonid Positselski, Alexander Slavik
The aim of this paper is to describe the classes of strongly flat and weakly cotorsion modules with respect to a multiplicative subset or a finite collection of multiplicative subs…
Flat morphisms of finite presentation are very flat
Leonid Positselski, Alexander Slavik
Principal affine open subsets in affine schemes are an important tool in the foundations of algebraic geometry. Given a commutative ring , -modules built from the rings of…