Iterated homotopy fixed points for the Lubin–Tate spectrum. With an appendix by Davis

with an appendix by daniel g. davis2 and ben wieland3 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 ho-motopy fixed point spectrum (ZhH)hK/H, where Z is a continuousG-spectrum and all group actions are to be continuous. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = bL(En∧X), where bL is Bousfield localization with respect to Morava K-theory, En is the Lubin-Tate spectrum, andX is any spectrum with trivialGn-action, then the iterated homotopy fixed point spectrum can always be constructed. Also, we show that (EhHn) hK/H is just EhKn, extending a result of Devinatz and Hopkins. 1