We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

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 …

We investigate parametrizations of compactly generated t-structures, or more generally, t-
structures with a definable coaisle, in the unbounded derived category $\mathrm …

We study the transfer of (co) silting objects in derived categories of module categories via
the extension functors induced by a morphism of commutative rings. It is proved that the …

We show that any homotopically smashing t-structure in the derived category of a
commutative noetherian ring is compactly generated. This generalizes the validity of the …

Over a commutative noetherian ring R, the prime spectrum controls, via the assignment of
support, the structure of both Mod (R) and D (R). We show that, just like in Mod (R), the …

We introduce a tensor compatibility condition for t-structures. For any Noetherian scheme X,
we prove that there is a one-to-one correspondence between the set of Thomason filtrations …

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 …

We show that compactly generated t-structures in the derived category of a commutative ring
R are in a bijection with certain families of compactly generated t-structures over the local …

We study the problem of when triangulated categories admit unique infinity-categorical
enhancements. Our results use Lurie's theory of prestable infinity-categories to give …