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Geometric and Functional Analysis

, Volume 26, Issue 5, pp 1449–1482 | Cite as

Fibrations with few rational points

  • D. LoughranEmail author
  • A. Smeets
Article

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.

Mathematics Subject Classification

14G05 14D10 11N36 11G35 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.School of MathematicsUniversity of ManchesterManchesterUK
  2. 2.Radboud University Nijmegen, IMAPPNijmegenThe Netherlands
  3. 3.Departement Wiskunde KU LeuvenLeuvenBelgium

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