Number Theory/Algebraic Geometry
P-adic weight pairings on pro-Jacobians
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 819-824.

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.

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.

Received:
Accepted:
Published online:
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, Volume 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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