Remarks on Kato's Euler systems for elliptic curves with additive reduction

JOURNAL OF NUMBER THEORY

卷:210

Article

Kim, Chan-Ho¹  Nakamura, Kentaro² 

[1] Korea Inst Adv Study, 85 Hoegiro, Seoul 02455, South Korea

[2] Saga Univ, Dept Math, 1 Honjo Machi, Saga 8408502, Japan

关键词: Elliptic curves;    Iwasawa theory;    Iwasawa main conjectures;    Kato's Euler systems;    Euler systems;    Kolyvagin systems;    Modular symbols;   

DOI  :  10.1016/j.jnt.2019.09.011

来源: Elsevier

【 摘 要 】

Extending the former work for the good reduction case, we provide a numerical criterion to verify a large portion of the Iwasawa main conjecture without p-adic L-functions for elliptic curves with additive reduction at an odd prime p over the cyclotomic Z(p)-extension. We also deduce the corresponding p-part of the Birch and Swinnerton-Dyer formula for elliptic curves of rank zero from the same numerical criterion. We give some explicit examples at the end and specify our choice of Kato's Euler system in the appendix. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free