An algebraic approach to Harder-Narasimhan filtrations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2018
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| _version_ | 1866909401402572800 |
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| author | Treffinger, Hipolito |
| author_facet | Treffinger, Hipolito |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_06322 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | An algebraic approach to Harder-Narasimhan filtrations Treffinger, Hipolito Category Theory Algebraic Geometry Rings and Algebras Representation Theory 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. |
| title | An algebraic approach to Harder-Narasimhan filtrations |
| topic | Category Theory Algebraic Geometry Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/1810.06322 |