### Abstract

Let n ≥ 1 and let p be any prime. Also, let E_{n} be the Lubin-Tate spectrum, G_{n} 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 L_{K(n)}(X) is equivalent to the homotopy fixed point spectrum (L_{K(n)}(E_{n} ∧ X))^{hG}_{n}, which is formed with respect to the continuous action of G_{n} on L_{K(n)}(E_{n} ∧ 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_{*}(L_{K(n)}(X)) is isomorphic to the descent spectral sequence that abuts to π_{*}((L_{K(n)}(E_{n} ∧ X))^{hG}_{n}).

Original language | English |
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Pages (from-to) | 1097-1103 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 140 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2012 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics