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La conjecture de Birch et Swinnerton-Dyer 𝐩 -adique

Pierre Colmez (2002/2003)

Séminaire Bourbaki

La conjecture de Birch et Swinnerton-Dyer prédit que l’ordre r du zéro en s = 1 de la fonction L d’une courbe elliptique E définie sur 𝐐 est égal au rang r du groupe de ses points rationnels. On sait démontrer cette conjecture si r = 0 ou 1 , mais on n’a aucun résultat reliant r et r si r 2 . Nous expliquerons comment Kato démontre que la fonction L p -adique attachée à E a, en s = 1 , un...

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