相关论文: Purity in compactly generated derivators and t-str…

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

In the setting of compactly generated triangulated categories, we show that the heart of a (co)silting t-structure is a Grothendieck category if and only if the (co)silting object satisfies a purity assumption. Moreover, in the cosilting…

We study when the heart of a t-structure in a triangulated category $\mathcal{D}$ with coproducts is AB5 or a Grothendieck category. If $\mathcal{D}$ satisfies Brown representability, a t-structure has an AB5 heart with an injective…

This paper is dedicated to the study of smashing weight structures (one may say that these are weight structures "coherent with arbitrary coproducts"), and the application of their properties to $t$-structures. In particular, we prove that…

We show that, under particular conditions, if a t-structure in the unbounded derived category of a locally coherent Grothendieck category restricts to the bounded derived category of its category of finitely presented objects, then its…

This thesis deals with the general problem of determining when the heart $\mathcal{H}$ of a t-structure in a triangulated category $\mathcal{D}$ is a Grothendieck or a module category. As preliminaries, we study Grothendieck conditions…

We study the behavior of direct limits in the heart of a t-structure. We prove that, for any compactly generated t-structure in a triangulated category with exact coproducts, countable direct limits are exact in its heart. Then, for a given…

Let $R$ be a commutative Noetherian ring and let $\mathcal D(R)$ be its (unbounded) derived category. We show that all compactly generated t-structures in $\mathcal D(R)$ associated to a left bounded filtration by supports of Spec$(R)$ have…

Starting with a Grothendieck category $\mathcal{G}$ and a torsion pair $\mathbf{t}=(\mathcal{T},\mathcal{F})$ in $\mathcal G$, we study the local finite presentability and local coherence of the heart $\mathcal{H}_{\mathbf{t}}$ of the…

Let $\mathcal{G}$ be a Grothendieck category, let $\mathbf{t}=(\mathcal{T},\mathcal{F})$ be a torsion pair in $\mathcal{G}$ and let $(\mathcal{U}_\mathbf{t},\mathcal{W}_\mathbf{t})$ be the associated Happel-Reiten-Smal$\o$ t-structure in…

The paper contains a collection of results related to weight structures, $t$-structures, and (more generally) to torsion pairs. For any weight structure $w$ we study (co)homological pure functors; these "ignore all weights except weight…

We give a classification theorem for a relevant class of $t$-structures in triangulated categories, which includes in the case of the derived category of a Grothendieck category, the $t$-structures whose hearts have at most $n$ fixed…

Given a locally coherent Grothendieck category G, we prove that the homotopy category of complexes of injective objects (also known as the coderived category of G) is compactly generated triangulated. Moreover, the full subcategory of…

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 [Hrb20,HHZ21]. We study the hearts of these two t-structures and prove that they…

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{\o} (HSR) t-structure in the derived category of a Grothendieck…

We show that the cotilting heart associated to a tilting complex $T$ is a locally coherent and locally coperfect Grothendieck category (i.e. an Ind-completion of a small artinian abelian category) if and only if $T$ is product-complete. We…

We study the t-structure induced by an n-tilting module T in the derived category D(R) of a ring R. Our main objective is to determine when the heart of the t-structure is a Grothendieck category. We obtain characterizations in terms of…

We show that, under mild conditions, the space of numerical Bridgeland stability conditions Stab(T) on a triangulated category T is complete. In particular the metric on a full component of Stab(T) for which the central charges factor…

We study a weight-exact localization pi of a well generated triangulated category C along with the embedding of the hearts of adjacent t-structures coming from the functor right adjoint to pi. We prove that the functors relating the…

We construct and study a candidate for the standard motivic t-structure on the triangulated category of relative cohomological 1-motives with rational coefficients over a noetherian finite dimensional scheme S. This t-structure is defined…