Jorge Vitoria (Verona)

Tilting theory and equivalences of recollements, I and II.

Abstract:

Recollements are useful decompositions of abelian or triangulated categories. Those in which all categories involved are module categories or their derived counterparts are of particular interest. One of the approaches to study such decompositions is the search for a "standard form", i.e., the search for a suitable representative in the equivalence class of a given recollement. In this talk we will present two solutions to this problem: one for recollements of module categories and one for recollements of derived categories of finite dimensional hereditary algebras. This will be done by analysing in detail all the important tools necessary to understand equivalences of recollements via tilting theory. In particular, we will review Morita theory for derived categories in some detail.