Rational points on pencils of conics and quadrics with many degenerate fibres

• 成果类型: Article
• 署名作者: Browning, T. D.; Matthiesen, L.; Skorobogatov, A. N.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2014.180.1.8
• 发表日期: 2014
• 页码: 381-402
• 关键词: hasse principle; weak approximation; descent; fibrations; bundles

摘要

For any pencil of conics or higher-dimensional quadrics over Q, with all degenerate fibres defined over Q, we show that the Brauer-Manin obs truction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics overQ, which is a consequence of recent advances in additive combinatorics.