Every K(n)-local spectrum is the homotopy fixed points of its Morava module

Daniel G. Davis, Takeshi Torii

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)1097-1103
Number of pages7
JournalProceedings of the American Mathematical Society
Volume140
Issue number3
DOIs
Publication statusPublished - 2012

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Local Spectrum
Homotopy
Fixed point
Module
Spectral Sequence
Morava K-theory
Point Spectrum
Descent
Isomorphic
Equivalence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Every K(n)-local spectrum is the homotopy fixed points of its Morava module. / Davis, Daniel G.; Torii, Takeshi.

In: Proceedings of the American Mathematical Society, Vol. 140, No. 3, 2012, p. 1097-1103.

Research output: Contribution to journalArticle

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