Computing canonical heights using arithmetic intersection theory

Müller, Jan

doi:10.1090/S0025-5718-2013-02719-6

Computing canonical heights using arithmetic intersection theory
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by Jan Steffen Müller;

Math. Comp. 83 (2014), 311-336

DOI: https://doi.org/10.1090/S0025-5718-2013-02719-6

Published electronically: June 14, 2013

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Abstract:

For several applications in the arithmetic of abelian varieties it is important to compute canonical heights. Following Faltings and Hriljac, we show how the canonical height of a point on the Jacobian of a smooth projective curve can be computed using arithmetic intersection theory on a regular model of the curve in practice. In the case of hyperelliptic curves we present a complete algorithm that has been implemented in Magma. Several examples are computed and the behavior of the running time is discussed.

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