Alexander Schmidt:

On the étale homotopy type of Morel-Voevodsky spaces

       Author: Alexander Schmidt
       Title: On the étale homotopy type of Morel-Voevodsky spaces
       Year: 2004
       Pages: 12

         Preliminary version: homotyp.dvi ,   homotyp.pdf
                          erratum   dvi     pdf


      Abstract:

In this paper we construct a natural extension of the functor "etale homotopy type" (defined by Artin and Mazur) from the category of smooth schemes over a field k to the category of simplicial etale sheaves on Sm/k. This functor factors through simplicial weak equivalences, thus induces a functor `etale homotopy type' on the simplicial homotopy category. Furthermore, if k has characteristic zero, then it factors over A^1-equivalence. As a result, we can attach étale homotopy groups to any (pointed) object of the A^1-homotopy category of smooth schemes over k (if k has characteristic zero).


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