Continuous homotopy fixed points for Lubin-Tate spectra

Abstract

We construct a stable model structure on profinite symmetric spectra with a continuous action of an arbitrary profinite group. This provides a natural framework for a new construction of homotopy fixed point spectra and of homotopy fixed point spectral sequences for the action of the extended Morava stabilizer group on Lubin-Tate spectra. These continuous homotopy fixed points are canonically equivalent to the homotopy fixed points of Devinatz and Hopkins but have a drastically simplified construction.

58 pages; revised and extended version containing more material on profinite G-spectra, stable profinite homotopy groups and homotopy limits, improved final section

References in corpus (1)

• The homotopy fixed point spectra of profinite Galois extensions

Cited by in corpus (1)

• Delta-discrete $G$-spectra and iterated homotopy fixed points