Quick, Gereon

Profinite homotopy theory

Doc. Math., J. DMV 13, 585-612 (2008)


Summary: 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.

Mathematics Subject Classification

55P60, 55Q70, 14F35


profinite completion, profinite homotopy groups, étale homotopy type of schemes