Silting subcategories and (co)torsion pairs associated to extended hearts

Abstract

We establish the poset isomorphisms between $(d+1)$-term silting subcategories, functorially finite $s$-torsion pairs in the $d$-extended heart, and hereditary complete cotorsion pairs in a suitable subcategory. As an application, we also give dg algebra versions of these bijections, which establish the poset isomorphisms between $\tau$-tilting pairs, $(d+1)$-term silting complexes, and functorially finite $s$-torsion pairs.

19 pages