Etale realization on the A^1-homotopy theory of schemes
K-Theory and Homology
2007-05-23 v2 Algebraic Topology
Abstract
We compare Friedlander's definition of the etale topological type for simplicial schemes to another definition involving realizations of pro-simplicial sets. This can be expressed as a notion of hypercover descent for etale homotopy. We use this result to construct a homotopy invariant functor from the category of simplicial presheaves on the etale site of schemes over S to the category of pro-spaces. After completing away from the characteristics of the residue fields of S, we get a functor from the Morel-Voevodsky A^1-homotopy category of schemes to the homotopy category of pro-spaces.
Keywords
Cite
@article{arxiv.math/0106158,
title = {Etale realization on the A^1-homotopy theory of schemes},
author = {Daniel C. Isaksen},
journal= {arXiv preprint arXiv:math/0106158},
year = {2007}
}