Recollements of (derived) module categories

Recollements of abelian, resp. triangulated, categories are exact sequences of abelian, resp. triangulated, categories where the inclusion functor as well as the quotient functor have left and right adjoints. They appear quite naturally in various settings and are omnipresent in representation theory. Recollements which all categories involved are module categories (abelian case) or derived categories of module categories (triangulated case) are of particular interest. In the abelian case, the "standard.example is the recollement induced by the module category of a ring R with an idempotent element e, and in the triangulated case the "standard.example is given as the derived counterpart of the previous recollement of module categories when the ideal ReR is stratifying. The latter recollement is called stratifying. The aim of this talk is two-fold. First, we classify, up to equivalence, recollements of abelian categories whose terms are equivalent to module categories. Then, we provide necessary and sufficient conditions for a recollement of derived categories of module categories over rings to be equivalent with a stratifying one and we discuss applications. This is joint work with Jorge Vitória.