Abstract
LetK=Fq(T) be a rational function field and ∞ the place given by the degree inT. LetL∞/K∞be a finite extension with ramification index not bigger than 2. We show in this paper how the local Néron–Tate height pairing at ∞ on Drinfeld modular curves overKof divisors whose points are defined overL∞can be described through analytic functions onΩ×ΩwhereΩis the Drinfeld upper half plane. The Green's function is locally constant around the cusps. ForX0(N) the Green's function for cusps is then described by Eisenstein series.
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