Continuous homotopy fixed points for Lubin-Tate spectra

TL;DR

This paper develops a new, simplified framework for constructing continuous homotopy fixed points of Lubin-Tate spectra with profinite group actions, enhancing the understanding of their spectral sequences.

Contribution

It introduces a stable model structure on profinite symmetric spectra with continuous group actions, enabling a more straightforward construction of homotopy fixed points for Lubin-Tate spectra.

Findings

Provides a natural framework for homotopy fixed point spectra

Simplifies the construction of homotopy fixed points

Establishes equivalence with Devinatz-Hopkins fixed points

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.