Sommaire

  • Cet exposé a été présenté le 08 décembre 2006.

Description

  • Orateur

    Christophe Ritzenthaler - Université de Luminy

Etant donnee une courbe (absolument irreductible, lisse, projective) de genre g sur un corps fini k, les questions du type : "quel peut etre son nombre maximal de points rationnels ? Quel peut etre son polynome du Frobenius ? Ou de maniere equivalente : quelles sont les classes d'isogenie de varietes abeliennes de dimension g sur k qui contiennent la jacobienne d'une courbe ?" sont d'importance, theoriques et pratiques. Nous verrons que les recherches sur ces questions suivant le cheminement naturel g=1,2 puis 3 font apparaitre successivement de nouveaux obstacles theoriques (et pas seulement calculatoires). Nous ferons en particulier le point sur une obstruction decouverte par Serre dans le cas du genre 3 non-hyperelliptique.

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