PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

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


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 $E$.


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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image