Fibrations with few rational points
D Loughran, A Smeets - Geometric and Functional Analysis, 2016 - Springer
Geometric and Functional Analysis, 2016•Springer
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.
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.
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.
Springer
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