Local Coherence of Hearts Associated with Thomason Filtrations

Abstract

Prompted by [S Š20], in which it is proved that the heart of a compactly generated t-structure in a triangulated category with coproduct is a locally finitely presented Grothendieck category, and inspired by [Hrb18], we study the local coherence of the hearts associated with Thomason filtrations of the prime spectrum of a commutative ring, achieving a useful recursive characterisation in case of finite length filtrations. Low length cases involve hereditary torsion classes of finite type of the ring, and even their Happel-Reiten-Smalø hearts; in these cases, the relevant characterisations are given by few module-theoretic conditions.