Handbook of Tilting Theory

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Good tilting modules and recollements of derived module categories (2010, background): “Infinite dimensional tilting theory has been of interest for a long time, but only recently it has increasingly attracted attention to understand derived categories of general rings and related topics (see [2, 4, 6, 7, 11, 12, 32]).”
Torsion classes, wide subcategories and localisations (2015, background): “T and F are chosen maximally with respect to the property that Hom(T,F)=0 for all T ∈ T and F ∈ F . When passing to module categories, torsion classes are studied, for example, in tilting theory (see [AHK]). In fact, the subcategory of all modules generated by a tilting module forms a torsion class.”
A silting theorem (2015, background): “t 35 years these ideas and concepts have become an essential tool in many branches of mathematics, including algebraic geometry, ﬁnite group theory, algebraic group theory and algebraic topology, see [AHK]. More recently, the development of cluster tilting theory, see [K, R], has spurred further int”
A complete derived invariant for gentle algebras via winding numbers and Arf invariants (2019, background): “In representation theory, different tools have been developed to handle this problem and have led to tilting theory [4].”