Parametrizing torsion pairs in derived categories

TL;DR

This paper explores parametrizations of t-structures in derived categories of rings, extending known constructions from commutative noetherian cases to more general settings, and classifies these structures over specific rings.

Contribution

It introduces a new construction of t-structures from chains of ring epimorphisms and provides classifications over certain classes of rings.

Findings

Constructed t-structures from chains of ring epimorphisms.

Provided methods to construct silting and cosilting objects.

Achieved classification results for specific ring classes.

Abstract

We investigate parametrizations of compactly generated t-structures, or more generally, t-structures with a definable coaisle, in the unbounded derived category D(Mod-A) of a ring A. To this end, we provide a construction of t-structures from chains in the lattice of ring epimorphisms starting in A, which is a natural extension of the construction of compactly generated t-structures from chains of subsets of the Zariski spectrum known for the commutative noetherian case. We also provide constructions of silting and cosilting objects in D(Mod-A). This leads us to classification results over some classes of commutative rings and over finite dimensional hereditary algebras.