Computing canonical heights using arithmetic intersection theory

Details Computing canonical heights using arithmetic intersection theory Computing canonical heights using arithmetic intersection theory

2011-05-09

arxiv.org/abs/1105.1719v3

Mathematics

Number Theory

29 pages. Fixed typos and minor errors, restructured some sections. Added new Example 3

Scientific paper

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 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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