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arXiv:2406.08017 (math)
[Submitted on 12 Jun 2024 (v1) , last revised 21 Aug 2025 (this version, v8)]

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

Title: 一个整体域上约化群的弱逼近缺陷

Authors:Mikhail Borovoi, Jean-Louis Colliot-Thélène
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.
Abstract: 我们根据群G的代数基本群来计算全局域K上约化群G的弱逼近缺陷。
Comments: v7: 27 pages, including the listing of a Magma program; v8: 29 pages, including an appendix by J.-L. Colliot-Th\'el\`ene
Subjects: Representation Theory (math.RT) ; Algebraic Geometry (math.AG); Group Theory (math.GR); Number Theory (math.NT)
MSC classes: 11E72, 20G10, 20G25, 20G30
Cite as: arXiv:2406.08017 [math.RT]
  (or arXiv:2406.08017v8 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.2406.08017
arXiv-issued DOI via DataCite
Journal reference: MPIM-Bonn-2024

Submission history

From: Mikhail Borovoi [view email]
[v1] Wed, 12 Jun 2024 09:17:59 UTC (14 KB)
[v2] Sat, 15 Jun 2024 18:54:32 UTC (14 KB)
[v3] Sat, 6 Jul 2024 13:42:46 UTC (15 KB)
[v4] Sun, 1 Sep 2024 14:59:45 UTC (15 KB)
[v5] Wed, 4 Sep 2024 05:45:26 UTC (15 KB)
[v6] Tue, 6 May 2025 10:38:23 UTC (19 KB)
[v7] Wed, 13 Aug 2025 10:07:24 UTC (20 KB)
[v8] Thu, 21 Aug 2025 12:55:44 UTC (21 KB)
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