Canonical heights on elliptic curves in characteristic p

1999/07/31 by Matthew A. Papanikolas
Mathematics · #math.NT #math.AG #msc:11G05 #msc:11G07 #msc:11R58 #msc:14G25

paper · pdf

published as Compositio Math. 122 (2000), 299-313 · 14 pages; final version

arxiv created 2001/06/08 · arxiv updated 2009/11/30

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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