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arXiv · 1004.4503

Computing Néron-Tate heights of points on hyperelliptic Jacobians

David Holmes
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Abstract

It was shown by Faltings and Hriljac that the Néron-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 Néron-Tate heights on Jacobians of hyperelliptic curves. To demonstrate the practicality of our algorithm, we illustrate it by computing Néron-Tate heights on Jacobians of hyperelliptic curves of genus from 1 to 9.

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David Holmes. 2017-05-02. Computing Néron-Tate heights of points on hyperelliptic Jacobians. https://doi.org/10.1016/j.jnt.2012.01.002

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