Homology, Homotopy and Applications

Volume 15 (2013)

Number 1

Profinite $G$-spectra

Pages: 151 – 189

DOI: https://dx.doi.org/10.4310/HHA.2013.v15.n1.a9

Author

Gereon Quick (Department of Mathematics, Harvard University, Cambridge, Mass., U.S.A.)

Abstract

We construct a stable model structure on profinite spectra with a continuous action of an arbitrary profinite group. The motivation is to provide a natural framework in a subsequent paper for a new and conceptually simplified construction of continuous homotopy fixed point spectra and of continuous homotopy fixed point spectral sequences for Lubin-Tate spectra under the action of the extended Morava stabilizer group.

Keywords

profinite space, profinite spectrum, continuous group action, profinite homotopy type

2010 Mathematics Subject Classification

55P43, 55Q70, 55Q91

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Published 1 May 2013