Luisa Fiorot
University of Padova

Tilting torsion classes, quasi-abelian categories and Auslander Formula.

Abstract:
Given an abelian category A its derived category D(A) admits a natural t-structure whose heart is A.
Moreover by the Auslander’s Formula A is equivalent to the quotient category of coherent functors by the Serre subcategory of effecable functors.
Given a quasi-abelian category E its derived category D(E) admits two canonical t-structures (left and right) whose hearts L and R are derived equivalent and their intersection in D(E) is E, moreover E is a tilting torsion class (rep. cotilting torsion-free class) in the right heart  R (resp.  L). We generalise the Auslander’s Formula proving that R (resp. L) can be described as the quotient category of covariant (resp. contravariant) coherent functors by the Serre subcategory of effecable functors.
Time permitting we extend this picture to its higher version using n—tilting torsion classe and n-quasi-abelian categories.