Continuous group actions on profinite spaces
Algebraic Topology
2010-11-08 v5 Algebraic Geometry
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 \'etale topological types of varieties over a field. One motivation is to understand Grothendieck's section conjecture in terms of homotopy fixed points.
Cite
@article{arxiv.0906.0245,
title = {Continuous group actions on profinite spaces},
author = {Gereon Quick},
journal= {arXiv preprint arXiv:0906.0245},
year = {2010}
}
Comments
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