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Sur le rang des Jacobiennes sur un corps de fonctions

Marc Hindry·Amílcar Pacheco
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Abstract

On the rank of Jacobians over function fields.} Let $f:\mathcal{X}\to C$ be a projective surface fibered over a curve and defined over a number field $k$. We give an interpretation of the rank of the Mordell-Weil group over $k(C)$ of the jacobian of the generic fibre (modulo the constant part) in terms of average of the traces of Frobenius on the fibers of $f$. The results also give a reinterpretation of the Tate conjecture for the surface $\mathcal{X}$ and generalizes results of Nagao, Rosen-Silverman and Wazir.

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Marc Hindry, Amílcar Pacheco. 2003-10-06. Sur le rang des Jacobiennes sur un corps de fonctions. https://arxiv.org/abs/math/0302184

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