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

Daniel C. Isaksen
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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.

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Daniel C. Isaksen. 2003-02-10. Etale realization on the A^1-homotopy theory of schemes. https://arxiv.org/abs/math/0106158

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