Local coherence of hearts associated with Thomason filtrations

Any Thomason filtration of a commutative ring yields (at least) two t-structures in the derived category ring, one which is compactly generated [19], [20]. We study hearts these and prove that they coincide case weakly bounded below filtration. Prompted by [39], it proved heart t-structure triangulated with coproduct locally finitely presented Grothendieck category, we local coherence associated filtration, achieving useful recursive characterisation finite length Low cases involve hereditary torsion classes type even their Happel–Reiten–Smalø hearts; cases, relevant characterisations are given few module-theoretic conditions.