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

Chan Ho Kim, Masato Kurihara

研究成果: Article査読

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
ページ(範囲)10559-10599
ページ数41
ジャーナルInternational Mathematics Research Notices
2021
14
DOI
出版ステータスPublished - 2021 7月 1

ASJC Scopus subject areas

  • 数学 (全般)

フィンガープリント

「On the Refined Conjectures on Fitting Ideals of Selmer Groups of Elliptic Curves with Supersingular Reduction」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル