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 introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-
cotilting modules. We prove that the three concepts AIR-cotilting modules, cosilting modules …

We give a generalization of the classical tilting theorem of Brenner and Butler. We show that
for a 2-term silting complex P in the bounded homotopy category K b (proj A) of finitely …

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 …

Let A be an abelian category and B be the Happel-Reiten-Smalø tilt of A with respect to a
torsion pair. We give necessary and sufficient conditions for the existence of a derived …

We study possible values of the global dimension of endomorphism algebras of 2-term
silting complexes. We show that for any algebra A whose global dimension gl. dim A≤ 2 …

arXiv:2212.09105v1 [math.RT] 18 Dec 2022 Page 1 arXiv:2212.09105v1 [math.RT] 18 Dec
2022 THERE ARE NO STRICTLY SHOD ALGEBRAS IN HEREDITARY GENTLE ALGEBRAS …

Let Λ be an Artin algebra and T a τ-tilting Λ-module. We prove that T is a tilting module if and
only if Ext Λ i (T, Fac T)= 0 for all i≥ 1, where Fac T is the full subcategory consisting of …

arXiv:2403.11359v1 [math.RT] 17 Mar 2024 Page 1 NAKAYAMA ALGEBRAS OF SMALL
HOMOLOGICAL DIMENSION AND PATTERN AVOIDING PERMUTATIONS VIKT ORIA KL ÁSZ1 …

Let A be a finite dimensional k-algebra and P a 2-term silting complex in K b (proj A). In this
article, we investigate the representation dimension of End D b (A)(P) by the silting theory …