We study connections between recollements of the derived category D (ModR) of a ring R
and tilting theory. We first provide constructions of tilting objects from given recollements …

Let T be an infinitely generated tilting module of projective dimension at most one over an
arbitrary associative ring A, and let B be the endomorphism ring of T. We prove that if T is …

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 …

We show that a tilting module T over a ring R admits an exact sequence 0→ R→ T 0→ T 1→
0 such that T_0,T_1∈Add(T) and Hom R (T 1, T 0)= 0 if and only if T has the form S⊕ S/R for …

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 show that silting modules are closely related with localizations of rings. More precisely,
every partial silting module gives rise to a localization at a set of maps between countably …

A Jordan–Hölder theorem is established for derived module categories of piecewise
hereditary algebras, in particular for representations of quivers and for hereditary abelian …

Recollements of triangulated categories may be seen as exact sequences of such
categories. Iterated recollements of triangulated categories are analogues of geometric or …

We give a complete classification of the infinite dimensional tilting modules over a tame
hereditary algebra R. We start our investigations by considering tilting modules of the form …

It is known that tilting classes are of finite type, while cotilting classes are not always of
cofinite type. We investigate this phenomenon. By using a bijection between definable …