Singular equivalences to locally coherent hearts of commutative noetherian rings

TL;DR

This paper establishes a connection between the derived categories of certain Grothendieck categories and commutative noetherian rings, demonstrating singular equivalences via tilting objects and Krause's recollement.

Contribution

It proves the existence of Krause's recollement for locally coherent Grothendieck categories with compactly generated derived categories and links it to singular equivalences in commutative noetherian rings.

Findings

Krause's recollement exists for these categories.

Tilting objects induce equivalences between recollements.

Singular equivalences are established for commutative noetherian rings.

Abstract

We show that Krause's recollement exists for any locally coherent Grothendieck category such that its derived category is compactly generated. As a source of such categories, we consider the hearts of intermediate and restrictable $t$-structures in the derived category of a commutative noetherian ring. We show that the induced tilting object over such a heart gives rise to an equivalence between the two Krause's recollements, and in particular, to a singular equivalence.