计算超椭圆雅可比簇上点的奈伦-泰特高度
数论
2017-05-03 v5
摘要
Faltings 和 Hriljac 证明了曲线上雅可比簇中点的奈伦-泰特高度可以表示为曲线正则模型上相应除子的自交数。我们使这一关系显式化，并利用它给出了一种计算超椭圆曲线雅可比簇上奈伦-泰特高度的算法。为了展示该算法的实用性，我们通过计算亏格从1到9的超椭圆曲线雅可比簇上的奈伦-泰特高度进行了说明。
引用
@article{arxiv.1004.4503,
title = {Computing N\'eron-Tate heights of points on hyperelliptic Jacobians},
author = {David Holmes},
journal= {arXiv preprint arXiv:1004.4503},
year = {2017}
}
备注
13 pages. v5: As kindly pointed out by Raymond van Bommel, the height is computed in this paper with respect to twice the theta divisor, not the theta divisor itself (as written in v4)