arXiv 1511.080272015-11math.NTmath.AG

Fibrations with few rational points

Daniel Loughran, Arne Smeets

备注：: 34 pages. Major revision. More details added and examples section moved to the end of the paper. Main theorems unchanged. To appear in GAFA

英文摘要：

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.

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