On the Asymptotic Growth of Bloch-Kato-Shafarevich-Tate Groups of Modular Forms Over Cyclotomic Extensions

被引：13

作者：

Lei, Antonio ^{[1
]}

Loeffler, David ^{[2
]}

Zerbes, Sarah Livia ^{[3
]}

机构：

[1] Univ Laval, Dept Math & Stat, Pavillon Alexandre Vachon, Quebec City, PQ G1V 0A6, Canada

[2] Univ Warwick, Math Inst, Zeeman Bldg, Coventry CV4 7AL, W Midlands, England

[3] UCL, Dept Math, Gower St, London WC1E 6BT, England

来源：

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES | 2017年 / 69卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

cyclotomic extension; Shafarevich-Tate group; Bloch-Kato Selmer group; modular form; non-ordinary prime; p-adic Hodge theory; P-ADIC REPRESENTATIONS; IWASAWA THEORY; ELLIPTIC-CURVES; SUPERSINGULAR REDUCTION; LOCAL-FIELD; PRIMES; VALUES;

D O I：

10.4153/CJM-2016-034-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the asymptotic behaviour of the Bloch-Kato-Shafarevich-Tate group of a modular form f over the cyclotomic Z(p)-extension of Q under the assumption that f is non-ordinary at p. In particular, we give upper bounds of these groups in terms of Iwasawa invariants of Selmer groups defined using p-adic Hodge Theory. These bounds have the same form as the formulae of Kobayashi, Kurihara, and Sprung for supersingular elliptic curves.

引用

页码：826 / 850

页数：25