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A Lyndon-Hochschild-Serre spectral sequence for certain homotopy fixed point spectra

Author: Ethan S. Devinatz
Translated by:
Journal: Trans. Amer. Math. Soc. 357 (2005), 129-150
MSC (2000): Primary 55N20; Secondary 55P43, 55T15
Published electronically: January 23, 2004
MathSciNet review: 2098089
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Abstract: Let $H$ and $K$ be closed subgroups of the extended Morava stabilizer group $G_n$ and suppose that $H$ is normal in $K$. We construct a strongly convergent spectral sequence

\begin{displaymath}H^\ast_c(K/H, (E^{hH}_n)^\ast X) \Rightarrow (E^{hK}_n)^\ast X, \end{displaymath}

where $E^{hH}_n$ and $E^{hK}_n$ are the continuous homotopy fixed point spectra of Devinatz and Hopkins. This spectral sequence turns out to be an Adams spectral sequence in the category of $K(n)_\ast$-local $E^{hK}_n$-modules.

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Additional Information

Ethan S. Devinatz
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195

Keywords: Adams spectral sequence, continuous homotopy fixed point spectra, Morava stabilizer group
Received by editor(s): September 13, 2002
Received by editor(s) in revised form: May 21, 2003
Published electronically: January 23, 2004
Additional Notes: The author was partially supported by a grant from the National Science Foundation.
Article copyright: © Copyright 2004 American Mathematical Society

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