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Comptes Rendus Mathématique
Volume 346, n° 15-16
pages 819-824 (août 2008)
Doi : 10.1016/j.crma.2008.06.005
Received : 28 Mars 2008 ;  accepted : 10 June 2008
P -adic weight pairings on pro-Jacobians
Accouplements de poids P -adiques sur les pro-jacobiennes

Daniel Delbourgo
School of Mathematical Sciences, Monash University, Melbourne, Victoria 3800, Australia 


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 Katoʼs zeta-elements with Λ -adic coefficients. To cite this article: D. Delbourgo, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

Soit E une courbe elliptique définie sur le corps des nombres rationnels. Nous proposons une méthode pour démontrer lʼénoncé
L(E,1)≠0implique#E(Q)<∞et#Eord<∞ en utilisant des formes modulaires p -adiques, cʼest-à-dire sans la théorie dʼIwasawa. La démonstration utilise une version des éléments-zêta à coefficients Λ -adiques. Pour citer cet article : D. Delbourgo, C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The full text of this article is available in PDF format.

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