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      Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction

      Delbourgo, Daniel; Lei, Antonio
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      Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction.pdf
      Accepted version, 420.1Kb
      DOI
       10.1017/S0305004115000535
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      Delbourgo, D., & Lei, A. (2015). Non-commutative Iwasawa theory for elliptic curves with multiplicative reduction. Mathematical Proceedings of the Cambridge Philosophical Society. http://doi.org/10.1017/S0305004115000535
      Permanent Research Commons link: https://hdl.handle.net/10289/10022
      Abstract
      Let E/ℚ be a semistable elliptic curve, and p ≠ 2 a prime of bad multiplicative reduction. For each Lie extension ℚ FT / ℚ with Galois group G∞ ≅ℤр ⋊ ℤ p ×, we construct p-adic L-functions interpolating Artin twists of the Hasse–Weil L-series of the curve E. Through the use of congruences, we next prove a formula for the analytic λ-invariant over the false Tate tower, analogous to Chern–Yang Lee's results on its algebraic counterpart. If one assumes the Pontryagin dual of the Selmer group belongs to the ℳℌ(G∞)-category, the leading terms of its associated Akashi series can then be computed, allowing us to formulate a non-commutative Iwasawa Main Conjecture in the multiplicative setting.
      Date
      2015
      Type
      Journal Article
      Publisher
      Cambridge University Press (CUP)
      Rights
      This is an author’s accepted version of an article published in the journal: Mathematical Proceedings of the Cambridge Philosophical Society. Copyright © Cambridge Philosophical Society 2015.
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      • Computing and Mathematical Sciences Papers [1455]
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