Profinite homotopy theory

Gereon Quick

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arXiv · 0803.4082

Profinite homotopy theory

Gereon Quick

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Abstract

We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and pro-spaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy groups fit well with the étale fundamental group which is always profinite. We show that the profinite étale topological realization functor is a good object in several respects.

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Gereon Quick. 2008-12-18. Profinite homotopy theory. https://arxiv.org/abs/0803.4082

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