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 …

In this paper we prove that any sheaf of modules over any topological space (in fact, any
$\mathcal {O} $-module where $\mathcal {O} $ is a sheaf of rings on the topological space) …

In this paper we prove the existence of a flat cover and a cotorsion envelope for any quasi-
coherent sheaf over the projective line, where R is any commutative ring. We first prove a …

We prove in this paper that for a quasi-compact and semi-separated (nonnecessarily
noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D (Aqc (X)) …

We describe an analogue of the notion of a perverse sheaf in the setting of the derived
category of coherent sheaves on an algebraic stack. Under strong additional assumptions …

I. Let E be an N-dimensional vector space over C (N~ 3), equipped with a nondegenerate
scalar product<,>,~ CP (N) be a square of isotropic lines, and B=@ H (Q,~(0) be the …

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 …

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]) …

Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …

We prove that the bounded derived category of coherent sheaves with proper support is
equivalent to the category of locally-finite, cohomological functors on the perfect derived …