Schinzel Hypothesis on average and rational points

• 成果类型: Article
• 署名作者: Skorobogatov, Alexei N.; Sofos, Efthymios
• 署名单位: Imperial College London; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences; University of Glasgow
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01153-6
• 发表日期: 2023
• 页码: 673-739
• 关键词: hasse principle; 2 quadrics; primes; intersections; progressions; VALUES

摘要

We resolve Schinzel's Hypothesis (H) for 100% of polynomials of arbitrary degrees. We deduce that a positive proportion of diagonal conic bundles over Q with any given number of degenerate fibres have a rational point, and obtain similar results for generalised Chatelet equations.