Drinfeld recently suggested to replace projective modules by the flat Mittag-Leffler ones in
the definition of an infinite dimensional vector bundle on a scheme X (Drinfeld, 2006 [8]) …

We show that over any ring, the double Ext-orthogonal class to all flat Mittag-Leffler modules
contains all countable direct limits of flat Mittag-Leffler modules. If the ring is countable, then …

The third and last of Philip Hall's seminal papers on finitely generated soluble groups
appeared in 1961 and had as its main positive result the theorem that the Frattini subgroup …

We put a monoidal model category structure on the category of chain complexes of quasi-
coherent sheaves over a quasi-compact and semi-separated scheme X. The approach …

Mittag-Leffler modules occur naturally in algebra, algebraic geometry, and model
theory,[20],[14],[19]. If R is a non-right perfect ring, then it is known that in contrast with the …

\S 0. Introduction. The main purpose of this paper is to extend some results on completely
reducible modules to quasi-injective modules by replacing “irreducible submodules” with …

A basic question for any property of quasi–coherent sheaves on a scheme $ X $ is whether
the property is local, that is, it can be defined using any open affine covering of $ X …

A module is called absolutely indecomposable if it is directly indecomposable in every
generic extension of the universe. We want to show the existence of large abelian groups …

Let $\mathbf {Ch}(\mathcal {O}) $ be the category of chain complexes of $\mathcal {O} $-
modules on a topological space $ T $(where $\mathcal {O} $ is a sheaf of rings on $ T $). We …

In this paper, we prove the existence of a flat cover and of a cotorsion envelope for any quasi-
coherent sheaf over a scheme (X, OX). Indeed we prove something more general. We define …