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The Tate-Shafarevich Group for Elliptic Curves with Complex Multiplication II

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Abstract

Using Iwasawa theory, we establish some numerical results, and one weak theoretical result, about the enigmatic Tate-Shafarevich group of an elliptic curve defined over the rational field, with complex multiplication. These strengthen results of this kind proven in an earlier paper of ours.

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Authors and Affiliations

  1. Emmanuel College, Cambridge, CB2 3AP, England

    J. Coates

  2. Department of Mathematics, POSTECH, Pohang, 790-784, Korea

    J. Coates

  3. School of Mathematical Sciences, Capital Normal University, Xisanhuanbeilu 105, Haidan District, Beijing, China

    Z. Liang

  4. School of Mathematics, TIFR, Homi Bhabha Road, Colaba, Mumbai, 40005, India

    R. Sujatha

Authors
  1. J. Coates
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  2. Z. Liang
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  3. R. Sujatha
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Corresponding author

Correspondence to J. Coates.

Additional information

Leonardo da Vinci Lecture held by John H. Coates on November 24, 2008

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Coates, J., Liang, Z. & Sujatha, R. The Tate-Shafarevich Group for Elliptic Curves with Complex Multiplication II. Milan J. Math. 78, 395–416 (2010). https://doi.org/10.1007/s00032-010-0127-2

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  • DOI: https://doi.org/10.1007/s00032-010-0127-2

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