Torsion models for tensor-triangulated categories: the one-step case
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909625570295808 |
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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 suitable stable monoidal model category $\mathscr{C}$ and a specialization closed subset $V$ of its Balmer spectrum one can produce a Tate square for decomposing objects into the part supported over $V$ and the part supported over $V^c$ spliced with the Tate object. Using this one can show that $\mathscr{C}$ is Quillen equivalent to a model built from the data of local torsion objects, and the splicing data lies in a rather rich category. As an application, we promote the torsion model for the homotopy category of rational circle-equivariant spectra from [18] to a Quillen equivalence. In addition, a close analysis of the one step case highlights important features needed for general torsion models which we will return to in future work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2011_10413 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Torsion models for tensor-triangulated categories: the one-step case Balchin, Scott Greenlees, J. P. C. Pol, Luca Williamson, Jordan Algebraic Topology Commutative Algebra Category Theory 55P60, 18G55, 13D, 55P91 Given a suitable stable monoidal model category $\mathscr{C}$ and a specialization closed subset $V$ of its Balmer spectrum one can produce a Tate square for decomposing objects into the part supported over $V$ and the part supported over $V^c$ spliced with the Tate object. Using this one can show that $\mathscr{C}$ is Quillen equivalent to a model built from the data of local torsion objects, and the splicing data lies in a rather rich category. As an application, we promote the torsion model for the homotopy category of rational circle-equivariant spectra from [18] to a Quillen equivalence. In addition, a close analysis of the one step case highlights important features needed for general torsion models which we will return to in future work. |
| title | Torsion models for tensor-triangulated categories: the one-step case |
| topic | Algebraic Topology Commutative Algebra Category Theory 55P60, 18G55, 13D, 55P91 |
| url | https://arxiv.org/abs/2011.10413 |