Fibrations with few rational points

Daniel Loughran; Arne Smeets

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arXiv · 1511.08027

Fibrations with few rational points

Daniel Loughran·Arne Smeets

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Abstract

We study the problem of counting the number of varieties in families which have a rational point. We give conditions on the singular fibres that force very few of the varieties in the family to contain a rational point, in a precise quantitative sense. This generalises and unifies existing results in the literature by Serre, Browning-Dietmann, Bright-Browning-Loughran, Graber-Harris-Mazur-Starr, et al.

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Daniel Loughran, Arne Smeets. 2015-11-25. Fibrations with few rational points. https://arxiv.org/abs/1511.08027

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