SÉMINAIRE DE THÉORIE DES NOMBRES 2002-2003

Le Vendredi à 15 heures 30 en Salle de Conférence

Organisateur : Laurent Herr



John Cremona
Nottingham
Saturation of Mordell-Weil groups.
RÉSUMÉ

The explicit computation of the Mordell-Weil group E(K) of an elliptic curve E defined over a number field K can be divided into two steps, watching the two stages in the proof that E(K) is finitely generated. In the first step (watching the weak Mordell-Weil Theorem), one computes E(K)/mE(K) for some m>1, by doing an m-descent (usually m=2). Generators for E(K) modulo mE(K) will generate a subgroup H of E(K) of finite index coprime to m. In the second step, one "saturates" this subgroup to obtain E(K) itself. In this talk, I will discuss joint work with current student Frickett and past student Siksek which make the second step practical. The ingredients include a local-global principle for p-divisibility in E(K) together with new lower bounds for the canonical height of a point in E(K).
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