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Etale realization on the A^1-homotopy theory of schemes
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
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