Simone Virili, Morita theory for stable derivators I and II.

Abstract:

The talk will be divided in two parts. In the first part we will review some of the basic definitions and examples in the theory of stable derivators. After that, we will recall the definition of a t-structure and show that t-structures on the base D(1) of a strong and stable derivator D are in bijection with (co)localizations of D. If time allows, we will mention some applications of this result as, for example, the fact that the heart of a compactly generated t-structure on the homotopy category of a stable model category (e.g., any algebraic or topological triangulated category), is a Grothendieck category. This is based on a joint work with Manuel Saorin and Jan Stovicek.

In the second part of the talk, we will start with a strong and stable derivator D, and a t-structure on the base D(1), whose heart we denote by A. We will then concentrate on the problem of comparing Der(A) (the unbounded derived category of the heart), with D(1). We will see that, under very mild assumptions one can always construct a morphism of prederivators, called realization morphism,

real : Der

where Der