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The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes

Volume 181 / 2017

Byoung Du Kim, Jeehoon Park Acta Arithmetica 181 (2017), 209-238 MSC: Primary 11G05, 11R23; Secondary 11G40. DOI: 10.4064/aa8606-8-2017 Published online: 1 December 2017

Abstract

Let $E$ be an elliptic curve over an abelian extension $F$ of an imaginary quadratic field $K$ with complex multiplication by $K$. Let $p$ be a prime number inert over $K/\mathbb Q$ (i.e. supersingular for $E$). We establish the main conjecture of Iwasawa theory under certain conditions on $p$. In other words, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus Selmer group of $E$ over the cyclotomic $\mathbb Z_p$-extension of $F$ is generated by the plus/minus $p$-adic $L$-function of $E$.

Authors

  • Byoung Du KimSchool of Mathematics and Statistics
    Victoria University of Wellington
    Wellington 6140, New Zealand
    e-mail
  • Jeehoon ParkDepartment of Mathematics
    Pohang University of Science and Technology
    77 Cheongam-Ro, Namgu
    Pohang, Gyeongbuk, 37673, South Korea
    e-mail

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