Duke Mathematical Journal

Iwasawa $L$-functions for multiplicative abelian varieties

John W. Jones

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Article information

Source
Duke Math. J. Volume 59, Number 2 (1989), 399-420.

Dates
First available: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077308008

Mathematical Reviews number (MathSciNet)
MR1016896

Zentralblatt MATH identifier
0716.14008

Digital Object Identifier
doi:10.1215/S0012-7094-89-05918-8

Subjects
Primary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10]
Secondary: 11G07: Elliptic curves over local fields [See also 14G20, 14H52] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture) 14K15: Arithmetic ground fields [See also 11Dxx, 11Fxx, 11G10, 14Gxx]

Citation

Jones, John W. Iwasawa L -functions for multiplicative abelian varieties. Duke Mathematical Journal 59 (1989), no. 2, 399--420. doi:10.1215/S0012-7094-89-05918-8. http://projecteuclid.org/euclid.dmj/1077308008.


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References

  • [1] D. Bernardi and C. Goldstein, Variante $p$-adique de la conjecture de Birch et Swinnerton-Dyer, C. R. Acad. Sci. Paris Sér. I Math. 301 (1985), no. 10, 455–458.
  • [2] D. Bernardi, C. Goldstein, and N. Stephens, Notes $p$-adiques sur les courbes elliptiques, J. Reine Angew. Math. 351 (1984), 129–170.
  • [3] S. Bosch and W. Lütkebohmert, Stable reduction and uniformization of abelian varieties II, Invent. Math. 78 (1984), no. 2, 257–297.
  • [4] R. Greenberg, Iwasawa theory for $p$-adic representations, to appear.
  • [5] J. Jones, Galois cohomology and parameterizations of semistable abelian varieties, manuscript.
  • [6] J. Jones, $p$-adic heights for semistable abelian varieties, Composito Math., to appear.
  • [7] B. Mazur, Rational points of abelian varieties with values in towers of number fields, Invent. Math. 18 (1972), 183–266.
  • [8] B. Mazur and J. Tate, Canonical height pairings via biextensions, Arithmetic and Geometry, Vol. I, Progr. Math., vol. 35, Birkhäuser, Boston, 1983, pp. 195–237.
  • [9] B. Mazur, J. Tate, and J. Teitelbaum, On $p$-adic analogues of the conjectures of Birch and Swinnerton-Dyer, Invent. Math. 84 (1986), no. 1, 1–48.
  • [10] W. McCallum, Duality theorems for Néron models, Duke Math. J. 53 (1986), no. 4, 1093–1124.
  • [11] A. Nasybullin, Elliptic Tate curves over local $\Gamma$-extensions, Math. Notes of U.S.S.R. 13 (1973), 322–327.
  • [12] B. Perrin-Riou, Descente infinie et hauteur $p$-adique sur les courbes elliptiques à multiplication complexe, Invent. Math. 70 (1982/83), no. 3, 369–398.
  • [13] P. Schneider, $p$-adic height pairings I, Invent. Math. 69 (1982), no. 3, 401–409.
  • [14] P. Schneider, Iwasawa $L$-functions of varieties over algebraic number fields: A first approach, Invent. Math. 71 (1983), no. 2, 251–293.
  • [15] P. Schneider, $p$-adic height pairings II, Invent. Math. 79 (1985), no. 2, 329–374.