|Responsables :||Zoé Chatzidakis, Raf Cluckers, Silvain Rideau.|
|Email des responsables :||email@example.com|
Pour recevoir le programme par e-mail, écrivez à : zchatzid_at_dma.ens.fr.
|Orateur(s)||Bas Edixhoven - Leiden,|
|Titre||Geometric quadratic Chabauty|
|Horaire||16:00 à 17:30|
Determining all rational points on a curve of genus at least 2 can be difficult. Chabauty's method (1941) is to intersect, for a prime number p, in the p-adic Lie group of p-adic points of the jacobian, the closure of the Mordell-Weil group with the p-adic points of the curve. If the Mordell-Weil rank is less than the genus then this method has never failed. Minhyong Kim's non-abelian Chabauty programme aims to remove the condition on the rank. The simplest case, called quadratic Chabauty, was developed by Balakrishnan, Dogra, Mueller, Tuitman and Vonk, and applied in a tour de force to the so-called cursed curve (rank and genus both 3). This article aims to make the quadratic Chabauty method small and geometric again, by describing it in terms of only `simple algebraic geometry' (line bundles over the jacobian and models over the integers).