Tuesday, December 15, 2020

Alexandra Zvonareva, 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^{2}A∩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. (Based on joint work with David Pauksztello.)