Insufficiency of the Brauer-Manin obstruction applied to etale covers

• 成果类型: Article
• 署名作者: Poonen, Bjorn
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 2157-2169
• 关键词: rational-points; chatelet surfaces; hasse-principle; 2 quadrics; intersections

摘要

Let k be any global field of characteristic not 2. We construct a k-variety X such that X(k) is empty, but for which the emptiness cannot be explained by the Brauer-Manin obstruction or even by the Brauer-Manin obstruction applied to finite etale covers.