Mathematics > Number Theory
[Submitted on 25 Nov 2015 (v1), last revised 29 Aug 2016 (this version, v2)]
Title:Fibrations with few rational points
View PDFAbstract: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.
Submission history
From: Daniel Loughran [view email][v1] Wed, 25 Nov 2015 12:07:40 UTC (31 KB)
[v2] Mon, 29 Aug 2016 08:51:44 UTC (32 KB)
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