### Etale realization on the A^1-homotopy theory of schemes, by Daniel C. Isaksen

We compare Friedlander's definition of etale homotopy for
simplicial schemes to another definition involving homotopy colimits 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.

Daniel C. Isaksen <isaksen.1@nd.edu>