# On the Refined Conjectures on Fitting Ideals of Selmer Groups of Elliptic Curves with Supersingular Reduction

Chan Ho Kim, Masato Kurihara

1 被引用数 (Scopus)

## 抄録

In this paper, we study the Fitting ideals of Selmer groups over finite subextensions in the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$ of an elliptic curve over $\mathbb{Q}$. Especially, we present a proof of the "weak main conjecture"à la Mazur and Tate for elliptic curves with good (supersingular) reduction at an odd prime $p$. We also prove the "strong main conjecture"suggested by the second named author under the validity of the $\pm$-main conjecture and the vanishing of a certain error term. The key idea is the explicit comparison among "finite layer objects", "$\pm$-objects", and "fine objects"in Iwasawa theory. The case of good ordinary reduction is also treated.

本文言語 English 10559-10599 41 International Mathematics Research Notices 2021 14 https://doi.org/10.1093/imrn/rnz129 Published - 2021 7月 1

• 数学 (全般)

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