An example of non-cotorsion Selmer group

King Fai Lai, Ignazio Longhi, Ki Seng Tan, Fabien Trihan

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Abstract

Let A/K be an elliptic curve over a global field of characteristic p > 0. We provide an example where the Pontrjagin dual of the Selmer group of A over a Γ := ℤp-extension L/K is not a torsion ℤp[[Γ]]-module and show that the Iwasawa Main Conjecture for A/L holds nevertheless.

Original languageEnglish
Pages (from-to)2355-2364
Number of pages10
JournalProceedings of the American Mathematical Society
Volume143
Issue number6
DOIs
Publication statusPublished - 2015

Keywords

  • Abelian variety
  • Frobenius
  • Iwasawa theory
  • Selmer group
  • Stickelberger element
  • Syntomic

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Lai, K. F., Longhi, I., Tan, K. S., & Trihan, F. (2015). An example of non-cotorsion Selmer group. Proceedings of the American Mathematical Society, 143(6), 2355-2364. https://doi.org/10.1090/S0002-9939-2015-12459-8