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Canonical heights and division polynomials

Published online by Cambridge University Press:  14 August 2014

ROBIN de JONG  and
J. STEFFEN MÜLLER
ROBIN de JONG
Affiliation:
Mathematisch Instituut, Universiteit Leiden, PO Box 9512, 2300 RA Leiden, The Netherlands. e-mail: rdejong@math.leidenuniv.nl
J. STEFFEN MÜLLER
Affiliation:
Institut für Mathematik, Carl von Ossietzky Universität Oldenburg, 26111 Oldenburg, Germany. e-mail: jan.steffen.mueller@uni-oldenburg.de
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 2 , September 2014 , pp. 357 - 373
Copyright
Copyright © Cambridge Philosophical Society 2014 

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