Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos

Email des responsables :

ziyang.gao@imj-prg.fr

Salle :

Adresse :

Description

http://www.imj-prg.fr/tn/STN/stnj.html

Orateur(s)

Alexandru Buium - ,

Titre

Independence of modular points on elliptic curves

Date

08/06/2009

Horaire

14:00 à 16:00

Résume

Given a correspondence between a modularcurve and an elliptic curve $A$ we show that there are not too manyrelations among the CM-points of $A$. In particular we show that theintersection of any finite rank subgroupof $A$ with the set of CM-points of $A$ is finite. We further analyse thisphenomenon by proving a local version of this global result with aneffective bound and valid also for certain infinite rank subgroups. Furthermore we will give similar local resultsfor intersections between subgroups of $A$ and isogeny classes in $A$.The local results are proved using a technique based on"arithmetic differential equations".All of this is joint work with B. Poonen.