The defect of weak approximation for a reductive group over a global field

2024/06/12 by Mikhail Borovoi, Borovoi, Mikhail, Colliot-Thélène, Jean-Louis
Mathematics · #11E72 #20G10 #20G25 #20G30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2406.08017

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the defect of weak approximation for a reductive group G over a global field K in terms of the algebraic fundamental group of G.

Related

• On Weak Approximation of Reductive Groups over Higher Dimensional Function Fields
• Obstructions to weak approximation for reductive groups over p-adic function fields
• The defect of weak approximation for homogeneous spaces. II
• Local-global principles for homogeneous spaces of reductive groups over global function fields
• On Almost Strong Approximation in Reductive Algebraic Groups