Geodesic
The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
Byoung Du Kim1 ; Jeehoon Park2
1 School of Mathematics and Statistics Victoria University of Wellington Wellington 6140, New Zealand
2 Department of Mathematics Pohang University of Science and Technology 77 Cheongam-Ro, Namgu Pohang, Gyeongbuk, 37673, South Korea
Acta Arithmetica, Tome 181 (2017) no. 3, pp. 209-238.

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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 $E$.
DOI : 10.4064/aa8606-8-2017
Keywords: elliptic curve abelian extension imaginary quadratic field complex multiplication prime number inert mathbb supersingular establish main conjecture iwasawa theory under certain conditions other words prove characteristic ideal pontryagin dual plus minus selmer group cyclotomic mathbb p extension generated plus minus p adic l function nbsp

Byoung Du Kim 1 ; Jeehoon Park 2

1 School of Mathematics and Statistics Victoria University of Wellington Wellington 6140, New Zealand
2 Department of Mathematics Pohang University of Science and Technology 77 Cheongam-Ro, Namgu Pohang, Gyeongbuk, 37673, South Korea 
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Byoung Du Kim; Jeehoon Park. The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes. Acta Arithmetica, Tome 181 (2017) no. 3, pp. 209-238. doi : 10.4064/aa8606-8-2017. http://geodesic.mathdoc.fr/articles/10.4064/aa8606-8-2017/

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