Iterated homotopy fixed points for the Lubin-Tate spectrum, with an Appendix: An example of a discrete G-spectrum that is not hyperfibrant
Abstract
When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not known, in general, how to form the iterated homotopy fixed point spectrum (ZhH)hK/H, where Z is a continuous G-spectrum and all group actions are to be continuous. However, we show that, if G=Gn, the extended Morava stabilizer group, and Z=LK(n)(En X), where LK(n) is Bousfield localization with respect to Morava K-theory, En is the Lubin-Tate spectrum, and X is any spectrum with trivial Gn-action, then the iterated homotopy fixed point spectrum can always be constructed. Also, we show that (EnhH)hK/H is just EnhK, extending a result of Devinatz and Hopkins.
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