Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups

Let G be a closed subgroup of the semi-direct product of the nth Morava stabilizer group S n with the Galois group of the field extension F p n / F p . We construct a “homotopy fixed point spectrum” E n hG whose homotopy fixed point spectral sequence involves the continuous cohomology of G. These sp...

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Bibliographic Details
Published in:Topology (Oxford) 2004, Vol.43 (1), p.1-47
Main Authors: Devinatz, Ethan S., Hopkins, Michael J.
Format: Article
Language:English
Subjects:
Adams spectral sequence
Commutative S-algebra
Continuous homotopy fixed point spectra
Morava stabilizer group
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Summary:Let G be a closed subgroup of the semi-direct product of the nth Morava stabilizer group S n with the Galois group of the field extension F p n / F p . We construct a “homotopy fixed point spectrum” E n hG whose homotopy fixed point spectral sequence involves the continuous cohomology of G. These spectra have the expected functorial properties and agree with the Hopkins-Miller fixed point spectra when G is finite.
ISSN:0040-9383
1879-3215
DOI:10.1016/S0040-9383(03)00029-6