We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …

We study t-structures with Grothendieck hearts on compactly generated triangulated
categories TT that are underlying categories of strong and stable derivators. This setting …

We explore the interplay between t‐structures in the bounded derived category of finitely
presented modules and the unbounded derived category of all modules over a coherent ring …

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 …

We establish a bijection between torsion pairs in the category of finite-dimensional modules
over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the …

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 …

It is a result of Gabriel that hereditary torsion pairs in categories of modules are in bijection
with certain filters of ideals of the base ring, called Gabriel filters or Gabriel topologies. A …

We show that Krause's recollement exists for any locally coherent Grothendieck category
whose derived category is compactly generated. As a source of such categories, we …

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 …