Fibrations with few rational points
Number Theory
2016-08-30 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1511.08027,
title = {Fibrations with few rational points},
author = {Daniel Loughran and Arne Smeets},
journal= {arXiv preprint arXiv:1511.08027},
year = {2016}
}
Comments
34 pages. Major revision. More details added and examples section moved to the end of the paper. Main theorems unchanged. To appear in GAFA