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.

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,

[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