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On the $ p$-adic heights of some abelian varieties


Author: Hideo Imai
Journal: Proc. Amer. Math. Soc. 100 (1987), 1-7
MSC: Primary 14K15; Secondary 11G10, 14G25
DOI: https://doi.org/10.1090/S0002-9939-1987-0883390-9
MathSciNet review: 883390
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Abstract: For an abelian variety defined over an algebraic number field, different definitions of $ p$-adic heights have been given by several authors. In this note, we shall prove that the $ p$-adic height defined by A. Néron and that by P. Schneider coincide.


References [Enhancements On Off] (What's this?)

  • [1] S. Bloch, A note on height pairings, Tamagawa numbers and the Birch and Swinnerton-Dyer conjecture, Invent. Math. 58 (1980), 65-76. MR 570874 (81m:14030)
  • [2] B. Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183-266. MR 0444670 (56:3020)
  • [3] B. Mazur and J. Tate, Canonical height pairing via biextensions, Arithmetic and Geometry (Volume dedicated to Shafarevich, vol. 1), Progress in Math., vol. 35, Birkhäuser, Boston, Basel, and Stuttgart, 1983, pp. 195-273. MR 717595 (85j:14081)
  • [4] A. Néron, Fonctions thêta $ p$-adiques et hauteurs $ p$-adiques (Séminaire de théorie de nombres, Paris 1980-1981), Progress in Math., vol. 22, Birkhäuser, Boston, Basel, and Stuttgart, 1982, pp. 149-174.
  • [5] J. Oesterlé, Construction de hauteurs archimediennes et $ p$-adiques suivant la methode de Bloch (Séminaire de théorie de nombres, Paris 1980-1981), Progress in Math., vol. 22, Birkhäuser, Boston, Basel, and Stuttgart, 1982, pp. 175-192. MR 693318 (85g:14055)
  • [6] B. Perrin-Riou, Hauteurs $ p$-adiques (Séminaire de théorie de nombres, Paris 1982-1983), Progress in Math., vol. 51, Birkhäuser, Boston, Basel, and Stuttgart, 1984, pp. 233-257. MR 791597 (87g:11072)
  • [7] P. Schneider, $ p$-adic height pairings. I, Invent. Math. 69 (1982), 401-409. MR 679765 (84e:14034)
  • [8] J. Tate, $ p$-divisible groups, Proceedings of a Conference on Local Fields, NUFFIC Summer School held at Driebergen, 1966, Springer, Berlin, Heidelberg, and New York, 1967, pp. 158-183. MR 0231827 (38:155)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0883390-9
Article copyright: © Copyright 1987 American Mathematical Society

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