Support $τ_2$-tilting and 2-torsion pairs

Abstract

The theory of τ -tilting was introduced by Adachi-Iyama-Reiten; one of the main results is a bijection between support τ -tilting modules and torsion classes. We are able to generalise this result in the context of the higher Auslander-Reiten theory of Iyama. For a finite-dimensional algebra A with 2-cluster-tilting subcategory C ⊆ modA, we are able to find a correspondence between support τ 2 -tilting A-modules and torsion pairs in C satisfying an additional functorial finiteness condition.