Profinite and discrete G –spectra and iterated homotopy fixed points

Profinite and discrete G –spectra and iterated homotopy fixed points
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有限和离散G谱和迭代同伦不动点

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通讯作者：
G. E. Q. Uick
G. E. Q. Uick
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作者：
D. A. G. D. Avis;G. E. Q. Uick

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对于定群G，令（-）hG、（-）hG和（-）h (cid:48) G分别为定群G谱、离散G谱和连续G谱（来自离散G谱塔）的连续同伦不动点。我们建立了前两个概念之间的一些联系，并利用Postnikov塔，对K (cid:67) c G（闭正规子群）给出了迭代同伦不动点（X hK） hG / K存在且为X hG的各种条件。对于Lubin-Tate谱E n和扩展的Morava稳定群G < c Gn，我们的结果表明，E hKn是一个具有（E hKn） hG / K (cid:39) E hGn的无限G / K谱，其论证具有（E hKn） hG / K (cid:39) E hGn所没有的技术简便性
For a profinite group G , let (-) hG , (-) h d G and (-) h (cid:48) G denote continuous homotopy fixed points for profinite G –spectra, discrete G –spectra and continuous G –spectra (coming from towers of discrete G –spectra), respectively. We establish some connections between the first two notions, and by using Postnikov towers, for K (cid:67) c G (a closed normal subgroup), give various conditions for when the iterated homotopy fixed points ( X hK ) hG / K exist and are X hG . For the Lubin–Tate spectrum E n and G < c G n , the extended Morava stabilizer group, our results show that E hKn is a profinite G / K –spectrum with ( E hKn ) hG / K (cid:39) E hGn , by an argument that possesses a certain technical simplicity not enjoyed by either the proof that ( E