Computing Néron-Tate heights of points on hyperelliptic Jacobians

Details Computing Néron-Tate heights of points on hyperelliptic Jacobians Computing Néron-Tate heights of points on hyperelliptic Jacobians

2010-04-26

arxiv.org/abs/1004.4503v4

Mathematics

Number Theory

13 pages. Rewritten and shortened

Scientific paper

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.

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