Let n ≥ 1 and let p be any prime. Also, let En be the Lubin-Tate spectrum, Gn the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the first author of this paper show that if X is a finite spectrum, then the localization LK(n)(X) is equivalent to the homotopy fixed point spectrum (LK(n)(En ∧ X))hGn, which is formed with respect to the continuous action of Gn on LK(n)(En ∧ X). In this paper, we show that this equivalence holds for any (S-cofibrant) spectrum X. Also, we show that for all such X, the strongly convergent Adams-type spectral sequence abutting to π*(LK(n)(X)) is isomorphic to the descent spectral sequence that abuts to π*((LK(n)(En ∧ X))hGn).
ASJC Scopus subject areas
- Applied Mathematics