2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78771We 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.14 pages; final versionNumber TheoryAlgebraic Geometry11G05, 11G07, 11R58, 14G25text