Rational points on fibrations with few non-split fibres

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-08 DOI:10.1515/crelle-2022-0042

Yonatan Harpaz, Dasheng Wei, Olivier Wittenberg

引用次数: 7

Abstract

Abstract We revisit the abstract framework underlying the fibration method for producing rational points on the total space of fibrations over the projective line. By fine-tuning its dependence on external arithmetic conjectures, we render the method unconditional when the degree of the non-split locus is ≤ 2 {\leq 2} , as well as in various instances where it is 3. We are also able to obtain improved results in the regime that is conditionally accessible under Schinzel’s hypothesis, by incorporating into it, for the first time, a technique due to Harari for controlling the Brauer–Manin obstruction in families.

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具有少量非分裂纤维的纤维上的有理点

我们重新审视了在投影线上的纤维化总空间上产生有理点的纤维化方法的抽象框架。通过微调其对外部算术猜想的依赖，当非分裂轨迹的程度≤2 {\leq 2}以及在它为3的各种情况下，我们使该方法成为无条件的。我们还能够在Schinzel假设下有条件地获得的制度中获得改进的结果，通过首次将哈拉里(Harari)用于控制家庭中的Brauer-Manin障碍的技术纳入其中。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.