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Canonical heights on elliptic curves in characteristic p

Matthew A. Papanikolas
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Abstract

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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Matthew A. Papanikolas. 2001-06-08. Canonical heights on elliptic curves in characteristic p. https://arxiv.org/abs/math/9907018

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