曲线函数域上动力小高度子簇的等分布
数论
2015-05-13 v3 动力系统
摘要
对于定义在域 上的射影簇 ，存在一类特殊的 自态射，称为代数动力系统。在本文中，我们取 为光滑曲线的函数域，并证明在 的每个赋值处， 中具有动力小高度的子簇在关联的 Berkovich 解析空间上是等分布的。我们仔细构建了陈述和证明该定理所需的所有算术相交理论，并提出了若干应用，涉及有界次数域扩张中预周期点和小高度点的非 Zariski 稠密性。
引用
@article{arxiv.0801.4811,
title = {Equidistribution of Dynamically Small Subvarieties over the Function Field of a Curve},
author = {X. W. C. Faber},
journal= {arXiv preprint arXiv:0801.4811},
year = {2015}
}
备注
v2: Various typos fixed; statement and proof of auxiliary Prop. 6.1 corrected. During the process of preparing this manuscript for submission, it came to the author's attention that Walter Gubler has recently proved many of the same results. See arXiv:0801.4508v3. v3: References updated and a few more typos corrected. To appear in Acta Arithmetica