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p-adic heights on abelian varieties. (English) Zbl 0707.14040
Sémin. Théor. Nombres, Paris/Fr. 1987-88, Prog. Math. 81, 317-341 (1990).
[For the entire collection see Zbl 0686.00006.]
The author explains how to unify two treatments of p-adic height- functions. In general one obtains a height-pairing on universal vector- extensions. One then splits the extensions (in the category of p-adic Lie-groups) using a splitting on de Rham cohomology. Such a splitting exists canonically for ordinary abelian varieties and also in the CM- case.
Reviewer: G.Faltings

14K15 Arithmetic ground fields for abelian varieties
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
14G20 Local ground fields in algebraic geometry
14K05 Algebraic theory of abelian varieties
14K22 Complex multiplication and abelian varieties