Equivariant Iwasawa theory for elliptic curves

被引：2
|
作者：
Kataoka, Takenori [1 ]
机构：
[1] Keio Univ, Fac Sci & Technol, Kohoku Ku, 3-14-1 Hiyoshi, Yokohama, Kanagawa 2238522, Japan
来源：
MATHEMATISCHE ZEITSCHRIFT | 2021年 / 298卷 / 3-4期
关键词：
Selmer groups; p-adic L-functions; Main conjecture; Mazur-Tate conjecture; KATOS EULER SYSTEM; SELMER GROUPS; SUPERSINGULAR PRIMES; CONJECTURES; BIRCH;
D O I：
10.1007/s00209-020-02666-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We discuss abelian equivariant Iwasawa theory for elliptic curves over Q at good supersingular primes and non-anomalous good ordinary primes. Using Kobayashi's method, we construct equivariant Coleman maps, which send the Beilinson-Kato element to the equivariant p-adic L-functions. Then we propose equivariant main conjectures and, under certain assumptions, prove one divisibility via Euler system machinery. As an application, we prove a case of a conjecture of Mazur-Tate.
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页码：1653 / 1725
页数：73
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