Implications of the Hasse Principle for Zero Cycles of Degree One on Principal Homogeneous Spaces

2010/10/07 by Jodi B. Black, Jodi Black, Black, Jodi
Computer Science · Mathematics · #11E57 #11E72 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Topological and Geometric Data Analysis #math.NT #msc:11E57 #msc:11E72

paper · pdf · doi:10.48550/arxiv.1010.1582

openalex publication_date 2010/10/07 · arxiv created 2010/10/08 · arxiv updated 2010/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a perfect field of virtual cohomological dimension ≤ 2. Let G be a connected linear algebraic group over k such that G^sc satisfies a Hasse principle over k. Let X be a principal homogeneous space under G over k. We show that if X admits a zero cycle of degree one, then X has a k-rational point.

Related

• Zero Cycles of Degree One on Principal Homogeneous Spaces
• An analytic viewpoint on the Hasse principle
• Linear spaces on hypersurfaces over number fields
• Local-global principle and integral Tate conjecture for certain varieties
• Local-global principle for 0-cycles on fibrations over rationally connected bases