Profinite homotopy theory
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 prospaces. 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 arXiv:
 arXiv:0803.4082
 Bibcode:
 2008arXiv0803.4082Q
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Algebraic Geometry;
 14F35;
 14H30;
 55P15
 EPrint:
 25 pages