2010/02/06 by Yonatan Harpaz, Harpaz, Yonatan, Tomer M. Schlank +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.1002.1423
This paper has been withdrawn by the author since the most recent version is in http://arxiv.org/abs/1110.0164
openalex publication_date 2010/02/06 · arxiv created 2011/11/30 · arxiv updated 2011/12/01 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
In 1969 Artin and Mazur defined the étale homotopy type of an algebraic variety \citeAMa69. In this paper we define various obstructions to the local-global principle on a variety X over a global field using the étale homotopy type of X and the concept of homotopy fixed points. We investigate relations between those "homotopy obstructions" and connect them to various known obstructions such as the Brauer -Manin obstruction, the étale-Brauer obstruction and finite descent obstructions. This gives a reinterpretation of known arithmetic obstructions in terms of homotopy theory.