Canonical heights on elliptic curves in characteristic p

Details Canonical heights on elliptic curves in characteristic p Canonical heights on elliptic curves in characteristic p

1999-07-02

arxiv.org/abs/math/9907018v2

Compositio Math. 122 (2000), 299-313

Mathematics

Number Theory

14 pages; final version

Scientific paper

We define a new canonical height pairing on the rational points of elliptic
curves over global function fields which takes values in the multiplicative
group of a completion of the function field. This height serves as an analogue
of both the classical Neron-Tate height and analytic p-adic heights. Our main
result is that under some general hypotheses this pairing is non-degenerate.

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