The category of rational $O(2)$-equivariant cohomology theories has an algebraic model $mathcal{A}(O(2))$, as established by work of Greenlees. That is, there is an equivalence of categories between the homotopy category of rational $O(2)$-equivariant spectra and the derived category of the abelian model $Dmathcal{A}(O(2))$. In this paper we lift this equivalence of homotopy categories to the level of Quillen equivalences of model categories. This Quillen equivalence is also compatible with the Adams short exact sequence of the algebraic model.
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机译:由Greenlees的工作建立的有理$ O(2)$-等变同调理论的类别具有$ mathcal {A}(O(2))$的代数模型。也就是说,在有理$ O(2)$等价谱的同伦范畴与阿贝尔模型$ D mathcal {A}(O(2))$的派生类别之间存在类别对等。在本文中,我们将同伦类别的等价性提升到模型类别的Quillen等价性的水平。这种Quillen等价关系也与代数模型的Adams短精确序列兼容。
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