REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: In this talk we will introduce the notion of mutation for certain objects in the derived category of a finite-dimensional algebra called cosilting complexes. These complexes roughly correspond to the injective cogenerators of hearts of t-structures in the derived category that are Grothendieck abelian categories e.g., hearts which are equivalent to module categories or categories of quasi-coherent sheaves. 

The focus of the talk will be on the case of two-term cosilting complexes, which parametrise the Grothendieck abelian hearts arising as HRS-tilts of torsion pairs in the module category. It turns out that two-term cosilting complexes also parametrise the torsion pairs in the category of finite-dimensional modules.  In 2014, Adachi-Iyama-Reiten showed that the irreducible mutations of two-term silting objects in the category of perfect complexes corresponds to minimal inclusions of functorially finite torsion classes.  We show that the irreducible mutations of two-term cosilting complexes in the derived category corresponds to minimal inclusions of arbitrary torsion classes.

This is part of ongoing joint work with Lidia Angeleri Hügel, Jan Stovicek and Jorge Vitória.