We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

Over a commutative noetherian ring $ R $, the prime spectrum controls, via the assignment
of support, the structure of both $\mathsf {Mod}(R) $ and $\mathsf {D}(R) $. We show that …

Let G be a locally coherent Grothendieck category. We show that, under particular
conditions, if a t-structure τ in the unbounded derived category D (G) restricts to the bounded …

We prove that, given any strong and stable derivator and a t-structure in its base triangulated
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …

Starting with a Grothendieck category G and a torsion pair t D. T; F/in G, we study the local
finite presentability and local coherence of the heart Ht of the associated Happel–Reiten …

In this paper we introduce the notion of pre-simple-minded collection (pre-SMC) of type
$\mathbb {A} $ in the bounded derived categories $\mathcal {D}^{b}(${\rm {\textbf {T}}} $ _p) …

We investigate conditions when the t-structure of Happel–Reiten–Smalø associated to a
torsion pair is a compactly generated t-structure. The concept of at CG torsion pair is …

In this paper we revisit the problem of determining when the heart of a t-structure is a
Grothendieck category, with special attention to the case of the Happel-Reiten-Smal …

Approximation theory is a fundamental tool in order to study the representation theory of a
ring R. Roughly speaking, it consists in determining suitable additive or abelian …

Any Thomason filtration of a commutative ring yields (at least) two t-structures in the derived
category of the ring, one of which is compactly generated [19],[20]. We study the hearts of …