Tuesday, May 21, 14:00, 7.527

Nico Stein, Resolution and realisation functors.

Abstract:
I will explain how to construct bounded and unbounded realisation functors of t-structures and resolution functors (=strong weight complex functors) of w-structures (=co-t-structures=weight structures) for algebraic triangulated categories. Under suitable assumptions, they yield an adjunction between the algebraic triangulated category and the derived category of the heart of the t-structure for adjacent t- and w-structures.
For silting and cosilting complexes, we obtain a connection between the derived categories of the heart of the associated t-structure and the module category that generalises the connection on the abelian level described by the silting and cosilting theorems for two-term complexes.
We also deduce a Morita theorem for derived categories of suitable abelian categories which include left-complete Grothendieck categories.