14 citations · 35 across the 5 of their papers we have counts for
7 papers
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…
On flat generators and Matlis duality for quasicoherent sheaves
Alexander Slávik, Jan Stovicek
We show that for a quasicompact quasiseparated scheme , the following assertions are equivalent: (1) the category of all quasicoherent sheaves on ha…
Purity in categories of sheaves
Alexander Slavik, Mike Prest
We consider categorical and geometric purity for sheaves of modules over a scheme satisfying some mild conditions, both for the category of all sheaves and for the category of quas…
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…
Quillen equivalent models for the derived category of flats and the resolution property
Sergio Estrada, Alexander Slavik
We investigate under which assumptions a subclass of flat quasi-coherent shea\-ves on a quasi-compact and semi-separated scheme allows to "mock" the homotopy category of projective…
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…