Séminaires : Séminaire Variétés Rationnelles

Equipe(s) : tga,
Responsables :Cyril Demarche et Mathieu Florence
Email des responsables :
Salle :
Adresse :Campus Pierre et Marie Curie
Description

 

Le séminaire a généralement lieu à Jussieu (Sorbonne Université, Paris), un vendredi par mois, entre 14h30 et 17h.

http://math.univ-lyon1.fr/homes-www/gille//sem/sem_variete_archives.html


Orateur(s) Bas Edixhoven - Leiden,
Titre Geometric interpretation of quadratic Chabauty
Date19/10/2018
Horaire15:00 à 16:00
Diffusion
RésumeJoint work with Guido Lido. Chabauty's method to find all rational points on a curve C over Q of genus g > 1 is to intersect, for a suitable prime p, inside the p-adic Lie group J(Q_p) (with J the jacobian of C), the 1-dimensional p-adic manifold C(Q_p) with the closure of J(Q). This closure is a p-adic Lie group of dimension at most r, the rank of J(Q). If r < g then this works well. Minhyong Kim has a program called "nonabelian Chabauty", where deeper quotients of the fundamental group of C are exploited (J corresponds to the abelianisation). The recently developed "quadratic Chabauty method" (Balakrishnan, Dogra, Muller, Tuitman, Vonk) can treat cases where r is larger and J has sufficiently many symmetric endomorphisms, notably the "cursed curve". In this lecture I will give a geometric description of the quadratic Chabauty method in terms of the Poincare torsor on J times its dual.
Salle
AdresseCampus Pierre et Marie Curie
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