Organizers: Matteo Longo, Nicola Mazzari, Luca Mastella, Khai-Hoan Nguyen-Dang
Time: The seminar will be held on Friday, room 2BC60, from 15:00-16:00. The first talk will take place on October 22.
Zoom:
ID: 827 1490 1749
Passcode: Please ask one of organizers for more information
The first part of the seminar will deal with Chabauty-Coleman method focusing on Coleman’s p-adic integration theory.
The second part will explain how Kim’s method is a natural generalization of the classical Chabauty.
Tentative Schedule
Talk I-October 22
Introduction to Chabauty, Chabauty-Coleman and Kim.
Speaker: Nicola Mazarri
Talk II-October 29
Construction of Coleman’s p-adic integration. [Col85a]
Speaker: Khai-Hoan Nguyen-Dang
Talk III-November 5
Coleman’s p-adic integration (cont). [Col85a]
Speaker: Khai-Hoan Nguyen-Dang
Talk IV-November 12
Coleman’s integration and torsion points. [MP12]
Speaker: Khai-Hoan Nguyen-Dang
Talk V-November 19
Effective Chabauty [Col85b]
If time permits: other effective applications of Chabauty-Coleman’s method in Diophantine equations [Sik13] or refinement of the bound [Sto06].
Speaker: Eduardo Rocha Walchek
Talk VI-November 26
Étalefundamental group. [Kim05]
Speaker: Pietro Vanni
Talk VII-December 5
The motivic fundamental group of P^1 - {0, 1, \infty} and the theorem of Siegel. [Kim05]
Speaker: Luca Mastella
Talk VIII-December 12
The motivic fundamental group of P^1 - {0, 1, \infty} and the theorem of Siegel (cont). [Kim05]
Speaker: Daniele Troletti
Talk IX- December 19
Selmer varieties and unipotent Albanese maps. [Kim09]
Speaker: Shilun Wang
[Bes12] A. Besser; Heidelberg lectures on coleman integration, In: The arithmetic of fundamental groups, (2012).
[Cha41] Claude Chabauty, Sur les points rationnels des courbes algebriques degenre superieura l’unite, C.R. Acad. Sci. Paris, (1941).
[Col85a] Robert F. Coleman, Torsion points on curves and p-adic abelian integrals, Ann. of Math, (1985).
[Col85b] Effective Chabauty, Duke Math. J., (1985).
[Kim05] Minhyong Kim. The motivic fundamental group of P^1∖{0,1,∞} and the theorem of Siegel. Invent. Math., (2005).
[Kim09] Minhyong Kim. The unipotent Albanese map and Selmer varieties for curves. Publ. Res. Inst.Math. Sci., (2009).
[MP12] The Method of Chabauty and Coleman, http://www-math.mit.edu/~poonen/papers/chabauty.pdf
[Sik13] S. Siksek; Explicit Chabauty over Number Fields, Algebra & Number Theory, (2013).
[Stol06] M. Stoll; Independence of rational points on twists of a given curve, Compositio Mathematica, (2006) .
Notes: The seminar notes update on 25 Novermber 2021. pdf