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arXiv · 1306.4030

Canonical heights and division polynomials

Robin de Jong·J. Steffen Müller
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Abstract

We discuss a new method to compute the canonical height of an algebraic point on a hyperelliptic jacobian over a number field. The method does not require any geometrical models, neither $p$-adic nor complex analytic ones. In the case of genus 2 we also present a version that requires no factorisation at all. The method is based on a recurrence relation for the `division polynomials' associated to hyperelliptic jacobians, and a diophantine approximation result due to Faltings.

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Robin de Jong, J. Steffen Müller. 2013-06-17. Canonical heights and division polynomials. https://doi.org/10.1017/s0305004114000371

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