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.
Lecturer
Date
18th September, 2025 ~ 15th January, 2026
Location
| Weekday | Time | Venue | Online | ID | Password |
|---|---|---|---|---|---|
| Thursday | 13:30 - 16:05 | A3-1a-205 | ZOOM 08 | 787 662 9899 | BIMSA |
Prerequisite
Some background on Algebraic geometry and Algebraic number theory will be helpful.
Reference
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.
Audience
Advanced Undergraduate
, Graduate
, Postdoc
, Researcher
Video Public
No
Notes Public
Yes
Language
English
Lecturer Intro
Yong Suk Moon joined BIMSA in 2022 fall as an assistant professor. His research area is number theory and arithmetic geometry. More specifically, his current research focuses on p-adic Hodge theory, Fontaine-Mazur conjecture, and p-adic Langlands program. He completed his Ph.D at Harvard University in 2016, and was a Golomb visiting assistant professor at Purdue University (2016-19) and a postdoctoral researcher at University of Arizona (2019 - 22).