Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On the $p$-adic heights of some abelian varieties
HTML articles powered by AMS MathViewer

by Hideo Imai PDF
Proc. Amer. Math. Soc. 100 (1987), 1-7 Request permission

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. NĂ©ron and that by P. Schneider coincide.
References
  • S. Bloch, A note on height pairings, Tamagawa numbers, and the Birch and Swinnerton-Dyer conjecture, Invent. Math. 58 (1980), no. 1, 65–76. MR 570874, DOI 10.1007/BF01402274
  • Barry Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183–266. MR 444670, DOI 10.1007/BF01389815
  • B. Mazur and J. Tate, Canonical height pairings via biextensions, Arithmetic and geometry, Vol. I, Progr. Math., vol. 35, Birkhäuser Boston, Boston, MA, 1983, pp. 195–237. MR 717595
    • A. NĂ©ron, Fonctions thĂŞta $p$-adiques et hauteurs $p$-adiques (SĂ©minaire de thĂ©orie de nombres, Paris 1980-1981), Progress in Math., vol. 22, Birkhäuser, Boston, Basel, and Stuttgart, 1982, pp. 149-174.
  • J. OesterlĂ©, Construction de hauteurs archimĂ©diennes et $p$-adiques suivant la methode de Bloch, Seminar on Number Theory, Paris 1980-81 (Paris, 1980/1981) Progr. Math., vol. 22, Birkhäuser Boston, Boston, MA, 1982, pp. 175–192 (French). MR 693318
  • B. Perrin-Riou, Hauteurs $p$-adiques, Seminar on number theory, Paris 1982–83 (Paris, 1982/1983) Progr. Math., vol. 51, Birkhäuser Boston, Boston, MA, 1984, pp. 233–257 (French). MR 791597
  • Peter Schneider, $p$-adic height pairings. I, Invent. Math. 69 (1982), no. 3, 401–409. MR 679765, DOI 10.1007/BF01389362
  • J. T. Tate, $p$-divisible groups, Proc. Conf. Local Fields (Driebergen, 1966) Springer, Berlin, 1967, pp. 158–183. MR 0231827
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14K15, 11G10, 14G25
  • Retrieve articles in all journals with MSC: 14K15, 11G10, 14G25
Additional Information
  • © Copyright 1987 American Mathematical Society
  • 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