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arXiv:math/9907018 [math.NT]AbstractReferencesReviewsResources

Canonical heights on elliptic curves in characteristic p

Matthew A. Papanikolas

Published 1999-07-02, updated 2001-06-08Version 2

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.

Comments: 14 pages; final version
Journal: Compositio Math. 122 (2000), 299-313
Categories: math.NT, math.AG
Subjects: 11G05, 11G07, 11R58, 14G25
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