2001/06/19 by Daniel C. Isaksen, Isaksen, Daniel C.
Mathematics · #14F35 (secondary) #14F42 (primary) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AT #math.KT #msc:14F35 #msc:14F42
paper · pdf · doi:10.48550/arxiv.math/0106158
openalex publication_date 2001/06/19 · arxiv created 2003/02/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 A1-homotopy category of schemes to the homotopy category of pro-spaces.