An algebraic approach to Harder-Narasimhan filtrations

In this article we study chains of torsion classes in an abelian category \(\mathcal{A}\). We prove that each chain of torsion classes induce a Harder-Narasimhan filtration for every nonzero object \(M\) in \(\mathcal{A}\), generalising a well-known property of stability conditions. We also characte...

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Veröffentlicht in:arXiv.org 2024-11
1. Verfasser: Treffinger, Hipolito
Format: Artikel
Sprache:eng
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Zusammenfassung:In this article we study chains of torsion classes in an abelian category \(\mathcal{A}\). We prove that each chain of torsion classes induce a Harder-Narasimhan filtration for every nonzero object \(M\) in \(\mathcal{A}\), generalising a well-known property of stability conditions. We also characterise the slicings of \(\mathcal{A}\) in terms of chain of torsion classes. We finish the paper by showing that chains of torsion classes induce wall-crossing formulas in the completed Hall algebra of the category.
ISSN:2331-8422
DOI:10.48550/arxiv.1810.06322