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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