Table of contents

  • This session has been presented October 21, 2005.

Description

  • Speaker

    Emmanuel Kowalski - Université Bordeaux I

La distribution du rang de familles de courbes elliptiques sur un corps de fonction sur un corps fini est théoriquement mieux comprise que dans le cas d'un corps de nombre. En particulier, dans le cas de familles de tordues quadratiques d'une courbe fixée, il est possible de montrer que le nombre de tordues dont le rang est plus grand que ce qu'impose l'équation fonctionnelle est trés petit. Les outils principaux sont des variantes uniformes du théorème de densité de Chebotarev et des calculs de monodromie de Katz. Les expériences numériques de telles situations sont, au contraire, trés peu développées ; si le temps le permet, on en dira quelques mots.

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