Fibrations with few rational points

D. Loughran, A. Smeets

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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.

Original languageEnglish
Pages (from-to)1449-1482
Number of pages34
JournalGeometric and Functional Analysis
Early online date12 Oct 2016
Publication statusPublished - 12 Oct 2016


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