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). |