We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme
is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More …

We study the behaviour of modules M that fit into a short exact sequence 0→ M→ C→ M→ 0,
where C belongs to a class of modules CC, the so-called C C-periodic modules. We find a …

The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the
behavior of the objects of cocycles in acyclic complexes. It is known that any flat Proj …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

A general principle suggests that" anything flat is a directed colimit of countably presentable
flats". In this paper, we consider resolutions and coresolutions of modules over a countably …

Let $ R $ be a ring and $\mathsf S $ be a class of strongly finitely presented (FP ${} _\infty $)
$ R $-modules closed under extensions, direct summands, and syzygies. Let $(\mathsf …

Contraherent cosheaves are module objects over algebraic varieties defined by gluing
using the colocalization functors. Contraherent cosheaves are designed to be used for …

In this paper, we study when the kernel of a complete hereditary cotorsion pair is the additive
closure of a tilting module. Applications go in three directions. The first is to characterize …

We consider a complete hereditary cotorsion pair (A, B) in a Grothendieck category G such
that A contains a generator of finite projective dimension. The derived category D (B) of the …

This paper is a follow-up to arXiv: 2212.09639. We consider an algebraic setting of
comodules over a coring, corresponding to a (noncommutative) algebraic geometry setting …