Support $τ_2$-tilting and 2-torsion pairs

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 $\mathcal{C}\subseteq\mathrm{mod}A$, we are able to find a correspondence between support $τ_2$-tilting $A$-modules and torsion pairs in $\mathcal{C}$ satisfying an additional functorial finiteness condition.

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