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Fibrations et conjecture de Tate

Marc Hindry·Amilcar Pacheco·Rania Wazir
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Abstract

We describe the behaviour of the rank of the Mordell-Weil group of the Picard variety of the generic fibre of a fibration in terms of local contributions given by averaging traces of Frobenius acting on the fibres. The results give a reinterpretation of Tate's conjecture (for divisors) and generalises previous results of Nagao, Rosen-Silverman and the authors.

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Marc Hindry, Amilcar Pacheco, Rania Wazir. 2004-02-02. Fibrations et conjecture de Tate. https://arxiv.org/abs/math/0311417

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