Etale realization on the A1-homotopy theory of schemes
By Daniel Isaksen. 2001
55 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3c7843fcb5f7903c7272f2db38dc00c6fab4824b
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Hypercovers and simplicial presheaves (2002, unknown): “In this final section we give a slight modification of Theorem 6· 2w hich isuseful in applications; for instance, it is needed in [ Is ].”
- Profinite homotopy theory (2008, methodology): “In fact, Isaksen shows that Et sends Nisnevich and étale hypercovers to weak equivalences in pro-S, [16], Theorem 12.”