HZ -algebra spectra are differential graded algebras
HZ -algebra spectra are differential graded algebras
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HZ -代数谱是微分分级代数
DOI：
10.1353/ajm.2007.0014
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发表时间：
2002
影响因子：
1.7
通讯作者：
B. Shipley
中科院分区：
文献类型：
--
作者：
B. Shipley
证明了微分分次代数的同伦理论与HZ-代数谱的同伦理论是一致的。即，我们构造了（无界）微分分次代数的Quillen模型范畴与HZ-代数谱之间的Quillen等价。我们还构造了这些代数上的微分分次模与模谱之间的Quillen等价。我们使用这些等价反过来产生代数模型的理性稳定的模型类别。我们表明，基本上任何合理的稳定的模型类别是Quillen等价于模块上的微分分次Q-代数（有许多对象）。
We show that the homotopy theory of differential graded algebras coincides with the homotopy theory of HZ-algebra spectra. Namely, we construct Quillen equivalences between the Quillen model categories of (unbounded) differential graded algebras and HZ-algebra spectra. We also construct Quillen equivalences between the differential graded modules and module spectra over these algebras. We use these equivalences in turn to produce algebraic models for rational stable model categories. We show that basically any rational stable model category is Quillen equivalent to modules over a differential graded Q-algebra (with many objects).