Torsion models for tensor-triangulated categories
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929668152623104 |
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| author | Balchin, Scott Greenlees, J. P. C. Pol, Luca Williamson, Jordan |
| author_facet | Balchin, Scott Greenlees, J. P. C. Pol, Luca Williamson, Jordan |
| contents | Given a rigidly-compactly generated tensor-triangulated category whose Balmer spectrum is finite dimensional and Noetherian, we construct a torsion model for it, which is equivalent to the original tensor-triangulated category. The torsion model is determined in an adelic fashion by objects with singleton supports. This categorifies the Cousin complex from algebra, and the process of reconstructing a spectrum from its monochromatic layers in chromatic stable homotopy theory. This model is inspired by work of the second author in rational equivariant stable homotopy theory, and extends previous work of the authors from the one-dimensional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05180 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Torsion models for tensor-triangulated categories Balchin, Scott Greenlees, J. P. C. Pol, Luca Williamson, Jordan Algebraic Topology Category Theory 55P60, 18G80, 18F99, 55P91 Given a rigidly-compactly generated tensor-triangulated category whose Balmer spectrum is finite dimensional and Noetherian, we construct a torsion model for it, which is equivalent to the original tensor-triangulated category. The torsion model is determined in an adelic fashion by objects with singleton supports. This categorifies the Cousin complex from algebra, and the process of reconstructing a spectrum from its monochromatic layers in chromatic stable homotopy theory. This model is inspired by work of the second author in rational equivariant stable homotopy theory, and extends previous work of the authors from the one-dimensional setting. |
| title | Torsion models for tensor-triangulated categories |
| topic | Algebraic Topology Category Theory 55P60, 18G80, 18F99, 55P91 |
| url | https://arxiv.org/abs/2501.05180 |