Fibrations et conjecture de Tate

Details Fibrations et conjecture de Tate Fibrations et conjecture de Tate

2003-11-24

arxiv.org/abs/math/0311417v2

Journal of Number Theory 112 (2005) 345 -- 368

Mathematics

Number Theory

21 pages, revised version

Scientific paper

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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