Filtrations of torsion classes in proper abelian subcategories
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913398159048704 |
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| author | Kortegaard, Anders S. |
| author_facet | Kortegaard, Anders S. |
| contents | In an abelian category $\mathscr{A}$, we can generate torsion pairs from tilting objects of projective dimension $\leq 1$. However, when we look at tilting objects of projective dimension $2$, there is no longer a natural choice of an associated torsion pair. Instead of trying to generate a torsion pair, Jensen, Madsen and Su generated a triple of extension closed classes that can filter any objects of $\mathscr{A}$. We generalize this result to proper abelian subcategories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13418 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Filtrations of torsion classes in proper abelian subcategories Kortegaard, Anders S. Representation Theory 18E10, 18G80 In an abelian category $\mathscr{A}$, we can generate torsion pairs from tilting objects of projective dimension $\leq 1$. However, when we look at tilting objects of projective dimension $2$, there is no longer a natural choice of an associated torsion pair. Instead of trying to generate a torsion pair, Jensen, Madsen and Su generated a triple of extension closed classes that can filter any objects of $\mathscr{A}$. We generalize this result to proper abelian subcategories. |
| title | Filtrations of torsion classes in proper abelian subcategories |
| topic | Representation Theory 18E10, 18G80 |
| url | https://arxiv.org/abs/2406.13418 |