Computing canonical heights using arithmetic intersection theory

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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 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.
Original languageEnglish
Pages (from-to)311-336
JournalMathematics of Computation
Volume83
DOIs
Publication statusPublished - 2014
Externally publishedYes

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