2011/10/02 by Yonatan Harpaz, Harpaz, Yonatan, Tomer M. Schlank +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #math.AT
paper · pdf · doi:10.48550/arxiv.1110.0164
arXiv admin note: substantial text overlap with arXiv:1002.1423
arxiv created 2011/10/02 · openalex publication_date 2011/10/02 · arxiv updated 2011/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we propose to use a relative variant of the notion of the étale homotopy type of an algebraic variety in order to study the existence of rational points on it. In particular, we use an appropriate notion of homotopy fixed points in order to construct obstructions to the local-global principle. The main results in this paper are the connections between these obstructions and the classical obstructions, such as the Brauer-Manin, the étale-Brauer and certain descent obstructions. These connections allow one to understand the various classical obstructions in a unified framework.