CANONICAL HEIGHTS ON ELLIPTIC CURVES IN CHARACTERISTIC p
نویسنده
چکیده
Let k = Fq(t) be the rational function field with finite constant field and characteristic p ≥ 3, and let K/k be a finite separable extension. For a fixed place v of k and an elliptic curveE/K which has ordinary reduction at all places ofK extending v, we consider a canonical height pairing 〈 , 〉v : E(K ) × E(K) → C v which is symmetric, bilinear and Galois equivariant. The pairing 〈 , 〉∞ for the “infinite” place of k is a natural extension of the classical Néron-Tate height. For v finite, the pairing 〈 , 〉v plays the role of global analytic p-adic heights. We further determine some hypotheses for the non-degeneracy of these pairings.
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