Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) Alexandru Buium - ,
Titre Independence of modular points on elliptic curves
Date08/06/2009
Horaire14:00 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.
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