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 …

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 …

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 …

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a
noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also …

REPORT ON THE FINITENESS OF SILTING OBJECTS Page 1 Proceedings of the Edinburgh
Mathematical Society (2021) 64, 217–233 doi:10.1017/S0013091521000109 REPORT ON THE …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …

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 …

We introduce the new concept of silting modules. These modules generalize tilting modules
over an arbitrary ring, as well as support-tilting modules over a finite dimensional algebra …

There are well-known constructions relating ring epimorphisms and tilting modules. The new
notion of silting module provides a wider framework for studying this interplay. To every …

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 …