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      Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions

      Delbourgo, Daniel; Lei, Antonio
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      ShaEstimates-v2.pdf
      Accepted version, 568.0Kb
      DOI
       10.1007/s11139-016-9785-1
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      Delbourgo, D., & Lei, A. (2017). Estimating the growth in Mordell-Weil ranks and Shafarevich-Tate groups over Lie extensions. Ramanujan Journal, 43(1), 29–68. https://doi.org/10.1007/s11139-016-9785-1
      Permanent Research Commons link: https://hdl.handle.net/10289/12260
      Abstract
      Let E/Q be an elliptic curve, p > 3 a good ordinary prime for E, and K∞ a p-adic Lie extension of a number field k. Under some standard hypotheses, we study the asymptotic growth in both the Mordell–Weil rank and Shafarevich–Tate group for E over a tower of extensions K ₙ/ₖ inside K∞; we obtain lower bounds on the former, and upper bounds on the latter’s size.
      Date
      2017
      Type
      Journal Article
      Publisher
      Springer
      Rights
      This is an author’s accepted version of an article published in the journal: The Ramanujan Journal. © Springer Science+Business Media New York 2016.
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      • Computing and Mathematical Sciences Papers [1455]
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