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Torsion models for
tensor-triangulated categories: the one-step case
Scott Balchin, John Greenlees, Luca Pol and Jordan Williamson |
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Algebraic & Geometric Topology 22 (2022) 2805–2856
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DOI: 10.2140/agt.2022.22.2805
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Abstract |
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Given a suitable stable monoidal model category and a specialization closed subset of its Balmer spectrum, one can produce a Tate square for decomposing objects into the part supported over and the part supported over spliced with the Tate object. Using this one can show that 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 of Greenlees (1999) 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. |
Keywords
algebraic model, tensor-triangulated category, Balmer
spectrum, rational equivariant spectra
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Mathematical Subject Classification
Primary: 55P60
Secondary: 13D09, 18N40, 55P91
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References |
Publication
Received: 8 December 2020
Revised: 11 June 2021
Accepted: 17 July 2021
Published: 13 December 2022
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Authors |
| Scott Balchin | |
| Max Planck Institute for
Mathematics Bonn Germany |
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| John Greenlees | |
| Mathematics Institute University of Warwick Coventry United Kingdom |
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| Luca Pol | |
| Fakultät für Mathematik Universität Regensburg Regensburg Germany |
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| Jordan Williamson | |
| Department of Algebra Charles University in Prague Praha Czech Republic |
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