有理等变稳定同伦论中的两面性
Ambidexterity in Rational Equivariant Stable Homotopy Theory
AI总结：
该研究证明有理真$G$-谱的$G$-范畴是参数化半加性的，将Wirthmüller同构扩展到更广泛的$G$-空间类，结合了两面性理论与参数化范畴论。
AI中文摘要：
我们证明，对于有限群$G$，有理真$G$-谱的$G$-范畴$\boldsymbol{\text{Sp}}_{G,\boldsymbol{\text{Q}}}$是参数化半加性的，依据是Cnossen–Lenz–Linskens的定义，针对真$G$-空间的态射，其不动点映射具有$\boldsymbol{\text{π}}$-有限纤维。特别地，这意味着由这类$G$-空间索引的有理真$G$-谱的余极限与极限之间的典范范数映射是等价的。这将Wirthmüller同构从$G$-轨道扩展到更广泛的$G$-空间类，并结合了Hopkins与Lurie的两面性理论和参数化范畴论。
英文摘要：
We show that for a finite group $G$, the $G$-category $\underline{\mathrm{Sp}}_{G,\mathbb{Q}}$ of rational genuine $G$-spectra is parametrized semiadditive, in the sense of Cnossen--Lenz--Linskens, for morphisms of genuine $G$-spaces whose fixed point maps have $π$-finite fibers. In particular, this means that the canonical norm map between a colimit and a limit of rational genuine $G$-spectra indexed by such $G$-spaces is an equivalence. This extends the Wirthmüller isomorphism from $G$-orbits to a broader class of $G$-spaces and combines the theory of ambidexterity of Hopkins and Lurie with parametrized category theory.
