Proceedings of the Japan Academy

A remark on the rational points of abelian varieties with values in cyclotomic $Z_p$-extensions

Hideo Imai

Full-text: Open access

Article information

Source
Proc. Japan Acad., Volume 51, Number 1 (1975), 12-16.

Dates
First available in Project Euclid: 20 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.pja/1195518722

Digital Object Identifier
doi:10.3792/pja/1195518722

Mathematical Reviews number (MathSciNet)
MR0371902

Zentralblatt MATH identifier
0323.14010

Subjects
Primary: 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]
Secondary: 12A65

Citation

Imai, Hideo. A remark on the rational points of abelian varieties with values in cyclotomic $Z_p$-extensions. Proc. Japan Acad. 51 (1975), no. 1, 12--16. doi:10.3792/pja/1195518722. https://projecteuclid.org/euclid.pja/1195518722


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References

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  • [2] Ju. Manin: Cyclotomic fields and modular curves. Russ. Math. Surveys, 26,7-78 (1971).
  • [3] B. Mazur: Rational points of abelian varieties with values in towers of number fields. Inventiones math., 18, 183-266 (1972).
  • [4] D. Mumford: Abelian Varieties. Oxford Univ. Press, London (1970).
  • [5] S. Sen: Lie algebras of Galois groups arising from Hodge-Tate modules. Ann. of Math., 07, 160-170 (1973).
  • [6] J.-P. Serre: Abelian i-adic representations and elliptic curves. Benjamin Inc. New York (1968).
  • [7] J.-P. Serre: Sur les groupes de Galois attaches aux groupes p-divisibles. Proceedings of a Conference on Local Fields, pp. 118-131. Springer, Berlin-Heidelberg-New York (1967).
  • [8] J.-P. Serre and J. Tate: Good reduction of abelian varieties. Ann. of Math., 88, 492-517 (1968).
  • [9] J. Tate: p-Divisible Groups. Proceedings of a Conference on Local Fields, pp. 158-183. Springer, Berlin-Heidelberg-New York (1967).