no. 15-16
Number Theory/Algebraic Geometry
P-adic weight pairings on pro-Jacobians
[Accouplements de poids P-adiques sur les pro-jacobiennes]

Présenté par : Christophe Soulé

Delbourgo, Daniel1
1 School of Mathematical Sciences, Monash University, Melbourne, Victoria 3800, Australia
Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 819-824.

Soit E une courbe elliptique définie sur le corps des nombres rationnels. Nous proposons une méthode pour démontrer l'énoncé

L(E,1)≠0implique#E(Q)<∞et#Eord<∞
en utilisant des formes modulaires p-adiques, c'est-à-dire sans la théorie d'Iwasawa. La démonstration utilise une version des éléments-zêta à coefficients Λ-adiques.

Let E denote an elliptic curve defined over the rational numbers. We outline a method of proving the statement

L(E,1)≠0implies both#E(Q)<∞and#Eord<∞
using properties of p-adic modular forms, i.e. no Iwasawa theory whatsoever. The proof employs a version of Kato's zeta-elements with Λ-adic coefficients.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.06.005
Delbourgo, Daniel 1

1 School of Mathematical Sciences, Monash University, Melbourne, Victoria 3800, Australia 
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Delbourgo, Daniel. P-adic weight pairings on pro-Jacobians. Comptes Rendus. Mathématique, Tome 346 (2008) no. 15-16, pp. 819-824. doi : 10.1016/j.crma.2008.06.005. http://www.numdam.org/articles/10.1016/j.crma.2008.06.005/

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