Chabauty-Kim method in Diophantine geometry
For a proper smooth curve over number field with genus bigger than 1, Mordell conjecture states that it has only finitely many rational points. The conjecture has been proved by Faltings, and later also by Vojta, Bombieri, and Lawrence-Venkatesh via different methods. A natural subsequent question is to understand an effective bound on the number of rational points. This course will be a gentle introduction to the Chabauty-Coleman and Chabauty-Kim method, which have been actively studied to obtain such a bound. Along with some theoretical background, we will go over concrete examples and computation.
讲师
日期
2025年09月18日 至 2026年01月15日
位置
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| 周四 | 13:30 - 16:05 | A3-1a-205 | ZOOM 08 | 787 662 9899 | BIMSA |
修课要求
Some background on Algebraic geometry and Algebraic number theory will be helpful.
参考资料
1. R. Coleman. "Effective Chabauty", "Torsion points on curves and p-adic abelian integrals"
2. M. Kim. "The motivic fundamental group of P1 \ {0,1,∞} and the theorem of Siegel", "The unipotent Albanese map and Selmer varieties for curves"
3. J. Balakrishnan - N. Dogra. "Quadratic Chabauty and rational points I: p-adic heights", "An effective Chabauty-Kim theorem"
4. More references can be found in Arizona Winter School 2020.
2. M. Kim. "The motivic fundamental group of P1 \ {0,1,∞} and the theorem of Siegel", "The unipotent Albanese map and Selmer varieties for curves"
3. J. Balakrishnan - N. Dogra. "Quadratic Chabauty and rational points I: p-adic heights", "An effective Chabauty-Kim theorem"
4. More references can be found in Arizona Winter School 2020.
听众
Advanced Undergraduate
, Graduate
, 博士后
, Researcher
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不公开
笔记公开
公开
语言
英文
讲师介绍
Yong Suk Moon于2022年秋作为助理研究员入职BIMSA。他的研究方向包括数论和算术几何。具体而言，他现在的研究集中在p-进霍奇理论，Fontaine-Mazur猜想和p-进Langlands纲领。他于2016年在哈佛大学取得博士学位，之后在普度大学作为访问助理教授工作3年，2019-2022年在美国亚利桑那大学做博士后。