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Title: Indivisibility of Kato's Euler systems and Kurihara numbers (Algebraic Number Theory and Related Topics 2018)
Authors: Kim, Chan-Ho
Ghitza, Alexandru
Keywords: 11F67
elliptic curues
Euler systems
Iwasawa main conjectures
Kato's Euler systems
Kurihara numbers
modular forms
modular symbols
Issue Date: Jul-2021
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Journal title: 数理解析研究所講究録別冊
Volume: B86
Start page: 63
End page: 86
Abstract: In this survey article, we discuss our recent work [KKS20], [KN20] on the numerical verification of the Iwasawa main conjecture for modular forms of weight two at good primes and elliptic curves with potentially good reduction. The criterion is based on the Euler system method and the equality of the main conjecture can be checked via the non-vanishing of Kurihara numbers. We also discuss further arithmetic applications of Kurihara numbers to study the structure of Selmer groups following the philosophy of refined Iwasawa theory `a la Kurihara. In the appendix by Alexandru Ghitza, the SageMath code for an effective computation of Kurihara numbers is illustrated.
Description: Algebraic Number Theory and Related Topics 2018. November 26-30, 2018. edited by Takao Yamazaki and Shuji Yamamoto. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.
Rights: © 2021 by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University. All rights reserved.
Appears in Collections:B86 Algebraic Number Theory and Related Topics 2018

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