Continuous group actions on profinite spaces

2009/06/01 by Gereon Quick, Quick, Gereon · 1 citation
Mathematics · #14F35 #55P91 #55Q70 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AG #math.AT #msc:14F35 #msc:55P91 #msc:55Q70

paper · pdf · doi:10.48550/arxiv.0906.0245

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

arxiv created 2010/11/04 · arxiv updated 2010/11/08

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.

Cited by

• On the real Section Conjecture in étale homotopy theory

Related

• Partial actions of groups on profinite spaces
• Continuous homotopy fixed points for Lubin-Tate spectra
• The homotopy fixed point spectra of profinite Galois extensions
• A homotopy orbit spectrum for profinite groups
• A lift from group cohomology to spectra for trivial profinite actions