Homology, Homotopy and Applications

Continuous homotopy fixed points for Lubin-Tate spectra

Gereon Quick

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Abstract

We provide a new and conceptually simplified construction of continuous homotopy fixed point spectra for Lubin-Tate spectra under the action of the extended Morava stabilizer group. Moreover, our new construction of a homotopy fixed point spectral sequence converging to the homotopy groups of the homotopy fixed points of Lubin-Tate spectra is isomorphic to an Adams spectral sequence converging to the homotopy groups of the spectra constructed by Devinatz and Hopkins. The new idea is built on the theory of profinite spectra with a continuous action by a profinite group.

Article information

Source
Homology Homotopy Appl., Volume 15, Number 1 (2013), 191-222.

Dates
First available in Project Euclid: 8 November 2013

Permanent link to this document
https://projecteuclid.org/euclid.hha/1383943674

Mathematical Reviews number (MathSciNet)
MR3079204

Zentralblatt MATH identifier
1278.55018

Subjects
Primary: 55P43: Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.) 55Q52: Homotopy groups of special spaces 55Q91: Equivariant homotopy groups [See also 19L47] 55T15: Adams spectral sequences

Keywords
Homotopy fixed point Lubin-Tate spectrum Morava stabilizer group Adams spectral sequence

Citation

Quick, Gereon. Continuous homotopy fixed points for Lubin-Tate spectra. Homology Homotopy Appl. 15 (2013), no. 1, 191--222. https://projecteuclid.org/euclid.hha/1383943674


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