Canonical heights on elliptic curves in characteristic p
Number Theory
2007-05-23 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.math/9907018,
title = {Canonical heights on elliptic curves in characteristic p},
author = {Matthew A. Papanikolas},
journal= {arXiv preprint arXiv:math/9907018},
year = {2007}
}
Comments
14 pages; final version