Iterated homotopy fixed points for the Lubin-Tate spectrum, with an Appendix: An example of a discrete G-spectrum that is not hyperfibrant

2006/10/29 by Daniel G. Davis, Davis, Daniel G., Ben Wieland +1
Mathematics · #55P42 #55T99 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P42 #msc:55T99

paper · pdf · doi:10.48550/arxiv.math/0610907

26 pages; added appendix (joint), which gives an example of a non-hyperfibrant discrete G-spectrum; Thm. 7.6 added; expanded Section 3; discussion of utility of K/H-action on E_n^hH added to Intro

arxiv created 2008/09/29 · arxiv updated 2009/12/01

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 homotopy fixed point spectrum (Z^hH)^hK/H, where Z is a continuous G-spectrum and all group actions are to be continuous. However, we show that, if G=G_n, the extended Morava stabilizer group, and Z=L_K(n)(E_n \wedge X), where L_K(n) is Bousfield localization with respect to Morava K-theory, E_n is the Lubin-Tate spectrum, and X is any spectrum with trivial G_n-action, then the iterated homotopy fixed point spectrum can always be constructed. Also, we show that (E_n^hH)^hK/H is just E_n^hK, extending a result of Devinatz and Hopkins.

Related

• Homotopy fixed points for L_K(n)(E_n ^ X) using the continuous action
• Every K(n)-local spectrum is the homotopy fixed points of its Morava module
• Continuous homotopy fixed points for Lubin-Tate spectra
• Several homotopy fixed point spectral sequences in telescopically localized algebraic K-theory
• Obtaining intermediate rings of a local profinite Galois extension without localization