We prove that the comparison map from $G$-fixed points to $G$-homotopy fixed points, for the $G$-fold smash power of a bounded below spectrum $B$, becomes an equivalence after $p$-completion if $G$ is a finite $p$-group and $H_{\ast }(B;{\mathbb{F}}_p)$ is of finite type. We also prove that the map becomes an equivalence after $I(G)$-completion if $G$ is any finite group and ${\pi }_{\ast }(B)$ is of finite type, where $I(G)$ is the augmentation ideal in the Burnside ring.

中文翻译：

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粉碎能力的西格尔猜想

我们证明比较图来自$G$- 固定指向$G$-同伦不动点，对于$G$- 有界以下频谱的折叠粉碎能力 $乙$, 变成等价的$p$-完成如果$G$是有限的$p$-组和$H_{＊}(乙;{\mathbb{F}}_p)$是有限类型的。我们还证明地图在之后变成等价的$我(G)$-完成如果$G$是任何有限群并且${\pi }_{＊}(乙)$是有限类型，其中$我(G)$是 Burnside 环中的增强理想。