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$$p$$-adic heights. (Hauteurs $$p$$-adiques.) (French) Zbl 0585.14017
Sémin. Théor. Nombres, Paris 1982–83, Prog. Math. 51, 233-257 (1984).
This paper is concerned with $$p$$-adic heights of rational points on an elliptic curve defined over a number field. The author first compares three different approaches to construct $$p$$-adic analogs of the Weierstraß $$\sigma$$-function, which lead to the definition of a $$p$$-adic height. She then introduces a “naive” $$p$$-adic height and shows that it is in fact a quadratic form. The relation between these $$p$$-adic heights has been investigated in a different paper of the author [C. R. Acad. Sci., Paris, Sér. I 296, 291–294 (1983; Zbl 0532.14012)].
For the entire collection see [Zbl 0541.00003].
Reviewer: Frank Herrlich
##### MSC:
 11G07 Elliptic curves over local fields 11G50 Heights 14G25 Global ground fields in algebraic geometry