On locally coherent hearts

Abstract

We show that, under particular conditions, if a t-structure in the unbounded derived category of a locally coherent Grothendieck category restricts to the bounded derived category of its category of finitely presented objects, then its heart is itself a locally coherent Grothendieck category. Those particular conditions are always satisfied when the Grothendieck category is arbitrary and one considers the t-structure associated to a torsion pair in the category of finitely presented objects. They are also satisfied when one takes any compactly generated t-structure in the derived category of a commutative noetherian ring which restricts to the bounded derived category of finitely generated modules. As a consequence, any t-structure in this latter bounded derived category has a heart which is equivalent to the category of finitely presented objects of some locally coherent Grothendieck category.

With respect to the previous version, an erroneous mention to hereditary torsion pair in Theorem 5.2 has been deleted

References in corpus (2)

• On purity and applications to coderived and singularity categories
• Addendum to 'Direct limits in the heart of a t-structure: The case of a torsion pair'

Cited by in corpus (5)

• Hearts for commutative noetherian rings: torsion pairs and derived equivalences
• Torsion pairs in categories of modules over a preadditive category
• Mutation and torsion pairs
• Singular equivalences to locally coherent hearts of commutative noetherian rings
• On cosilting hearts over the Kronecker algebra