HRS tilting for co-t-structures and cotorsion pairs
abstract:
In this talk I will explain how to construct a new
co-t-structure from a given co-t-structure (A,B) and a complete
cotorsion pair in its extended co-heart
C=Σ^2A∩B. This construction is similar to the Happel-Reiten-Smalo
tilt of a t-structure with respect to a torsion pair in its heart
and it induces a bijection between intermediate co-t-structures
and complete cotorsion pairs. For a finite dimensional
algebra this introduces a new component to the numerous existing
bijections studied in tau-tilting theory and in silting theory,
that is the bijections between intermediate algebraic
t-structures, functorially finite torsion pairs, two-term silting
complexes, and so on.