相关论文: Hearts of t-structures which are Grothendieck or m…

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…

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…

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…

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…

Given a torsion pair $\mathbf{t} = (\mathcal{T} ;\mathcal{F})$ in a module category $R$-Mod we give necessary and sufficient conditions for the associated Happel-Reiten-Smal\o $\text{ }$ t-structure in $\mathcal{D}(R)$ to have a heart…

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…

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…

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…

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 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…

We study t-structures with Grothendieck hearts on compactly generated triangulated categories $\mathcal{T}$ that are underlying categories of strong and stable derivators. This setting includes all algebraic compactly generated triangulated…

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…

This paper classifies t-structures on the local derived category of a 3-fold flopping contraction, that are intermediate with respect to the heart of perverse coherent sheaves. Equivalently, this describes the complete lattice of torsion…

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, just like in $\mathsf{Mod}(R)$, the assignment of support…

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…

We give necessary and sufficient conditions for torsion pairs in a hereditary category to be in bijection with $t$-structures in the bounded derived category of that hereditary category. We prove that the existence of a split $t$-structure…

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the derived category D(Mod R). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with…

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…

Let $T$ be a $1$-tilting module whose tilting torsion pair $({\mathcal T}, {\mathcal F})$ has the property that the heart ${\mathcal H}_t$ of the induced $t$-structure (in the derived category ${\mathcal D}({\rm Mod} \mbox{-} R)$ is…

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…