Continuous group actions on profinite spaces

Abstract

For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point space and for stable homotopy groups of homotopy orbit spaces. Our main example is the Galois action on profinite étale topological types of varieties over a field. One motivation is to understand Grothendieck's section conjecture in terms of homotopy fixed points.

26 pages; revision of the proof of the main theorem; final version to appear in JPAA; this time with a new file uploaded, so this is v4

References in corpus (1)

• The real section conjecture and Smith's fixed point theorem for pro-spaces

Cited by in corpus (1)

• The Étale Homotopy Type and Obstructions to the Local-Global Principle