Beyond heights: slopes and distribution of rational points
Number Theory
2018-07-31 v2 Algebraic Geometry
Abstract
The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise the points in these thin subsets. The slopes introduced by Jean-Beno\^it Bost are a useful tool for this problem. These notes will present several cases in which this approach is fruitful. We shall also describe the notion of locally accumulating subvarieties which arises when one considers rational points of bounded height near a fixed rational point.
Keywords
Cite
@article{arxiv.1806.11437,
title = {Beyond heights: slopes and distribution of rational points},
author = {Emmanuel Peyre},
journal= {arXiv preprint arXiv:1806.11437},
year = {2018}
}
Comments
53 pages, improved and completed version, with the correction of many minor mistakes