Recollements and stratifying ideals

TL;DR

This paper investigates when recollements of derived categories can be characterized by stratifying ideals, providing criteria, constructions, and a negative answer to their universal applicability.

Contribution

It offers a characterization of recollements equivalent to stratifying ones and criteria for stratifying ring epimorphisms, advancing understanding of derived category decompositions.

Findings

Not all recollements are equivalent to stratifying ones.

Criteria for stratifying ring epimorphisms are established.

Constructive methods for stratifying epimorphisms are provided.

Abstract

Surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories. These `stratifying' recollements are derived from recollements of module categories. Can every recollement be put in this form, up to equivalence? A negative answer will be given after providing a characterisation of recollements equivalent to stratifying ones. Moreover, criteria for a ring epimorphism to be `stratifying' will be presented as well as constructions of such epimorphisms.