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Currently displaying 1 – 3 of 3

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Autour d'une conjecture de Serge Lang.

Marc Hindry — 1988

Inventiones mathematicae

Géométrie arithmétique

Marc Hindry — 1993

Cahiers du séminaire d'histoire des mathématiques

Sur le rang des jacobiennes sur un corps de fonctions

Marc Hindry; Amílcar Pacheco — 2005

Bulletin de la Société Mathématique de France

Soit $f : 𝒳 \to C$ une surface projective fibrée au-dessus d’une courbe et définie sur un corps de nombres $k$ . Nous donnons une interprétation du rang du groupe de Mordell-Weil sur $k (C)$ de la jacobienne de la fibre générique (modulo la partie constante) en termes de moyenne des traces de Frobenius sur les fibres de $f$ . L’énoncé fournit une réinterprétation de la conjecture de Tate pour la surface $𝒳$ et généralise des résultats de Nagao, Rosen-Silverman et Wazir.

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