The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication

被引：2

作者：

Hara, Takashi ^{[1
]}

Ochiai, Tadashi ^{[2
]}

机构：

[1] Tokyo Denki Univ, Sch Sci & Technol Future Life, Tokyo 1208551, Japan

[2] Osaka Univ, Grad Sch Sci, Osaka 5600043, Japan

来源：

KYOTO JOURNAL OF MATHEMATICS | 2018年 / 58卷 / 01期

关键词：

ADIC L-FUNCTIONS; TOTALLY-REAL FIELDS; MODULAR-FORMS; SPECIAL VALUES; CM FIELDS; ELLIPTIC-CURVES; ZETA-FUNCTIONS; SELMER GROUP; REPRESENTATIONS; CONGRUENCE;

D O I：

10.1215/21562261-2017-0018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We deduce the cyclotomic Iwasawa main conjecture for Hilbert modular cusp forms with complex multiplication from the multivariable main conjecture for CM number fields. To this end, we study in detail the behavior of the p-adic L-functions and the Selmer groups attached to CM number fields under specialization procedures.

引用

页码：1 / 100

页数：100

共 43 条

[11] ON THE LIFTING OF HILBERT CUSP FORMS TO HILBERT-HERMITIAN CUSP FORMS
Yamana, Shunsuke
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (08) : 5395 - 5438
[12] MULTIPLICATIVE REDUCTION AND THE CYCLOTOMIC MAIN CONJECTURE FOR GL2
Skinner, Christopher
PACIFIC JOURNAL OF MATHEMATICS, 2016, 283 (01) : 171 - 200
[13] ON THE "MAIN CONJECTURE" OF EQUIVARIANT IWASAWA THEORY
Ritter, Juergen
Weiss, Alfred
JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 24 (04) : 1015 - 1050
[14] ON THE IWASAWA MAIN CONJECTURE FOR THE DOUBLE PRODUCT
Delbourgo, Daniel
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 377 (09) : 6225 - 6250
[15] Heegner Point Kolyvagin System and Iwasawa Main Conjecture
Wan, Xin
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2021, 37 (01) : 104 - 120
[16] On the Iwasawa main conjecture for generalized Heegner classes in a quaternionic setting
Pati, Maria Rosaria
FORUM MATHEMATICUM, 2025, 37 (01) : 225 - 245
[17] On the two-variable Iwasawa main conjecture
Ochiai, Tadashi
COMPOSITIO MATHEMATICA, 2006, 142 (05) : 1157 - 1200
[18] Iwasawa-Greenberg main conjecture for nonordinary modular forms and Eisenstein congruences on GU(3,1)
Castella, Francesc
Liu, Zheng
Wan, Xin
FORUM OF MATHEMATICS SIGMA, 2022, 10
[19] ANALOGUES OF IWASAWA'S μ=0 CONJECTURE AND THE WEAK LEOPOLDT CONJECTURE FOR A NON-CYCLOTOMIC Z2-EXTENSION
Choi, Junhwa
Kezuka, Yukako
Li, Yongxiong
ASIAN JOURNAL OF MATHEMATICS, 2019, 23 (03) : 383 - 400
[20] AN EQUIVARIANT MAIN CONJECTURE IN IWASAWA THEORY AND THE COATES-SINNOTT CONJECTURE
Taleb, Reza
DOCUMENTA MATHEMATICA, 2013, 18 : 749 - 783

← 1 2 3 4 5 →