Duke Mathematical Journal

Mordell-Weil groups of elliptic curves over C(t) with pg=0 or 1

David A. Cox

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Article information

Source
Duke Math. J., Volume 49, Number 3 (1982), 677-689.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077315384

Digital Object Identifier
doi:10.1215/S0012-7094-82-04935-3

Mathematical Reviews number (MathSciNet)
MR672502

Zentralblatt MATH identifier
0503.14018

Subjects
Primary: 14K07
Secondary: 14J25: Special surfaces {For Hilbert modular surfaces, see 14G35} 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]

Citation

Cox, David A. Mordell-Weil groups of elliptic curves over $\mathbf{C}(t)$ with $p_g=0$ or $1$. Duke Math. J. 49 (1982), no. 3, 677--689. doi:10.1215/S0012-7094-82-04935-3. https://projecteuclid.org/euclid.dmj/1077315384


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References

  • [1] D. A. Cox and W. R. Parry, Torsion in elliptic curves over $k(t)$, Compositio Math. 41 (1980), no. 3, 337–354.
  • [2] D. A. Cox and S. Zucker, Intersection numbers of sections of elliptic surfaces, Invent. Math. 53 (1979), no. 1, 1–44.
  • [3] E. Horikawa, Surjectivity of the period map of $\rm K3$ surfaces of degree $2$, Math. Ann. 228 (1977), no. 2, 113–146.
  • [4a] K. Kodaira, On compact analytic surfaces. II, Ann. of Math. (2) 77 (1963), 563–626.
  • [4b] K. Kodaira, On compact analytic surfaces. III, Ann. of Math. (2) 78 (1963), 1–40.
  • [5] J. Milnor and D. Husemoller, Symmetric bilinear forms, Springer-Verlag, New York, 1973.
  • [6] I. I. Pjateckiĭ-Šapiro and I. R. Šafarevič, Torelli's theorem for algebraic surfaces of type $\rm K3$, Izv. Akad. Nauk SSSR Ser. Mat. 35 (1971), 530–572.
  • [7] T. Shioda, On elliptic modular surfaces, J. Math. Soc. Japan 24 (1972), 20–59.