Profinite and discrete G–spectra and iterated homotopy fixed points

Abstract

Abstract. For a profinite group G, let (-) hG , (-) h d G , and (-) h ′ 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 ⊳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 En and G <c Gn, the extended Morava stabilizer group, our results show that E hK n is a profinite G/K-spectrum with (E hK n ) hG/K ≃ E hG n , by an argument that possesses a certain technical simplicity not enjoyed by either the proof that (E h ′ K n