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arXiv · 0906.0245

Continuous group actions on profinite spaces

Gereon Quick
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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.

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Gereon Quick. 2010-11-04. Continuous group actions on profinite spaces. https://arxiv.org/abs/0906.0245

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