Computing N\'eron-Tate heights of points on hyperelliptic Jacobians
Number Theory
2017-05-03 v5
Abstract
It was shown by Faltings and Hriljac that the N\'eron-Tate height of a point on the Jacobian of a curve can be expressed as the self-intersection of a corresponding divisor on a regular model of the curve. We make this explicit and use it to give an algorithm for computing N\'eron-Tate heights on Jacobians of hyperelliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing N\'eron-Tate heights on Jacobians of hyperelliptic curves of genus from 1 to 9.
Keywords
Cite
@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}
}
Comments
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)