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- W4301017589 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." @default.
- W4301017589 created "2022-10-04" @default.
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- W4301017589 date "2003-02-17" @default.
- W4301017589 modified "2023-10-01" @default.
- W4301017589 title "Sur le rang des Jacobiennes sur un corps de fonctions" @default.
- W4301017589 doi "https://doi.org/10.48550/arxiv.math/0302184" @default.
- W4301017589 hasPublicationYear "2003" @default.
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