Torsion pairs via cosilting mutation
Representation Theory
2026-02-23 v1 Rings and Algebras
Abstract
For a left artinian ring A, we study the lattice torsA of torsion pairs in the category of finitely generated A-modules by considering an isomorphic lattice formed by certain closed sets in a topological space associated to A, the Ziegler spectrum of the unbounded derived category of ModA. Torsion pairs in torsA turn out to be adjacent if and only if the associated closed sets are related by an operation which is induced by mutation of cosilting complexes. We describe this operation from several perspectives and present a number of applications in the case when A is a finite dimensional algebra.
Cite
@article{arxiv.2602.18341,
title = {Torsion pairs via cosilting mutation},
author = {Lidia Angeleri Hügel},
journal= {arXiv preprint arXiv:2602.18341},
year = {2026}
}
Comments
This is a survey on recent joint work with Rosanna Laking, Francesco Sentieri, Jan \v{S}\v{t}ov\'{\i}\v{c}ek, and Jorge Vit\'oria