Fibrations with few rational points

D. Loughran, A. Smeets

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.
Original languageEnglish
Pages (from-to)1449-1482
Number of pages34
JournalGeometric and Functional Analysis
Volume26
Issue number5
DOIs
Publication statusPublished - 1 Oct 2016

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