DERIVED CATEGORIES AND TILTING

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Good tilting modules and recollements of derived module categories (2010, background): “The theory of finitely generated tilting modules has been suc cessfully applied, in the representation theory of algebras and groups, to understanding different aspects of algebraic structure and homological features of (algebraic) groups, algebras and modules (for instance, se e [13, 15, 16, 21], [”
Braid groups and Kleinian singularities (2009, background): “For instance, we may take D to be the homotopy category of a stable ∞category in the sense of [12], an algebraic triangulated category in the sense of [8], or a pre-triangulated differential-graded category in the sense of [2].”
The Stable Monomorphism Category of a Frobenius category (2009, background): “We have a well-behaved notion of tilting object for an algebraical triangulated category ([21]).”
The periodicity conjecture for pairs of Dynkin diagrams (2010, unknown): “[66], [34], [45].”