Homology, Homotopy and Applications

Volume 15 (2013)

Number 1

Continuous homotopy fixed points for Lubin-Tate spectra

Pages: 191 – 222

DOI: http://dx.doi.org/10.4310/HHA.2013.v15.n1.a10

Author

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

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.

Keywords

homotopy fixed point, Lubin-Tate spectrum, Morava stabilizer group, Adams spectral sequence

2010 Mathematics Subject Classification

55P43, 55Q52, 55Q91, 55T15

Full Text (PDF format)