Fibrations with few rational points

By Daniel Loughran, Arne Smeets. Geometric and Functional Analysis, 2015

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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.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1eb2d007717a39acb1f997edab48d14d142a308c