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

Chan Ho Kim, Masato Kurihara

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1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)10559-10599
Number of pages41
JournalInternational Mathematics Research Notices
Volume2021
Issue number14
DOIs
Publication statusPublished - 2021 Jul 1

ASJC Scopus subject areas

  • Mathematics(all)

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