Torsion models for tensor-triangulated categories: the one-step case
Torsion models for tensor-triangulated categories: the one-step case
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DOI：
10.2140/agt.2022.22.2805
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发表时间：
2020-11
期刊：
影响因子：
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通讯作者：
Scott Balchin;J. Greenlees;Luca Pol;J. Williamson
中科院分区：
文献类型：
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作者：
Scott Balchin;J. Greenlees;Luca Pol;J. Williamson
给定一个合适的稳定monoidal模型范畴$\mathscr{C}$和它的Balmer谱的一个特化闭子集$V$，我们可以产生一个Tate方，用于将对象分解为支持在$V$上的部分和支持在$V^c$上的部分，并与Tate对象拼接。使用这个可以表明$\mathscr{C}$是Quillen等价于从局部扭转对象的数据建立的模型，并且拼接数据属于相当丰富的类别。作为应用，我们将文[16]中有理圆等变谱同伦范畴的挠模型推广到Quillen等价。此外，一个步骤的情况下，一个密切的分析突出了一般扭转模型所需的重要功能，我们将在未来的工作中返回。
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 [16] 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.