Duke Mathematical Journal

Torsion points on elliptic curves over all quadratic fields

S. Kamienny

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J. Volume 53, Number 1 (1986), 157-162.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077304886

Mathematical Reviews number (MathSciNet)
MR835802

Zentralblatt MATH identifier
0599.14029

Digital Object Identifier
doi:10.1215/S0012-7094-86-05310-X

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 14G25: Global ground fields 14K07

Citation

Kamienny, S. Torsion points on elliptic curves over all quadratic fields. Duke Mathematical Journal 53 (1986), no. 1, 157--162. doi:10.1215/S0012-7094-86-05310-X. http://projecteuclid.org/euclid.dmj/1077304886.


Export citation

References

  • [1] P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), Springer, Berlin, 1973, 143–316. Lecture Notes in Math., Vol. 349.
  • [2] H. Farkas and I. Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York, 1980.
  • [3] B. Gross and D. Rohrlich, Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), no. 3, 201–224.
  • [4] S. Kamienny, Modular curves and unramified extensions of number fields, Compositio Math. 47 (1982), no. 2, 223–235.
  • [5] S. Kamienny, On $J\sb{1}(p)$ and the conjecture of Birch and Swinnerton-Dyer, Duke Math. J. 49 (1982), no. 2, 329–340.
  • [6] S. Kamienny, Points of order $p$ on elliptic curves over ${\bf Q}(\sqrt{p})$, Math. Ann. 261 (1982), no. 4, 413–424.
  • [7] S. Kamienny, Rational points on modular curves and abelian varieties, J. Reine Angew. Math. 359 (1985), 174–187.
  • [8] D. Kubert and S. Lang, Modular units, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 244, Springer-Verlag, New York, 1981.
  • [9] B. Mazur, Modular curves and the Eisenstein ideal, Inst. Hautes Études Sci. Publ. Math. (1977), no. 47, 33–186 (1978).
  • [10] B. Mazur, 1979, Letter to A. Ogg dated March 6.
  • [11] B. Mazur and J. Tate, Points of order $13$ on elliptic curves, Invent. Math. 22 (1973/74), 41–49.
  • [12] A. Ogg, Hyperelliptic modular curves, Bull. Soc. Math. France 102 (1974), 449–462.
  • [13] F. Oort and J. Tate, Group schemes of prime order, Ann. Sci. École Norm. Sup. (4) 3 (1970), 1–21.
  • [14] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo, 1971.
  • [15] G. Stevens, The cuspidal group and special values of $L$-functions, preprint.