Fibrations with few rational points

Research output: Contribution to journalArticle

  • Authors:
  • D. Loughran
  • A. Smeets


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.

Bibliographical metadata

Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalGeometric and Functional Analysis
Early online date12 Oct 2016
StatePublished - 2016