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

[1] On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights
Wang, Haining
ANNALES MATHEMATIQUES DU QUEBEC, 2023, 47 (01): : 195 - 248
[2] Anticyclotomic Iwasawa's Main Conjecture for Hilbert modular forms
Longo, Matteo
COMMENTARII MATHEMATICI HELVETICI, 2012, 87 (02) : 303 - 353
[3] Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
Angles, Bruno
Bandini, Andrea
Bars, Francesc
Longhi, Ignazio
MATHEMATISCHE ANNALEN, 2020, 376 (1-2) : 475 - 523
[4] On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights
Haining Wang
Annales mathématiques du Québec, 2023, 47 : 195 - 248
[5] On the anticyclotomic Iwasawa main conjecture for modular forms
Chida, Masataka
Hsieh, Ming-Lun
COMPOSITIO MATHEMATICA, 2015, 151 (05) : 863 - 897
[6] On the main conjecture of Iwasawa theory for certain non-cyclotomic Zp-extensions
Kezuka, Yukako
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2019, 100 (01): : 107 - 136
[7] Some remarks on the two-variable main conjecture of Iwasawa theory for elliptic curves without complex multiplication
Van Order, Jeanine
JOURNAL OF ALGEBRA, 2012, 350 (01) : 273 - 299
[8] On the Dihedral Main Conjectures of Iwasawa Theory for Hilbert Modular Eigenforms
Van Order, Jeanine
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2013, 65 (02): : 403 - 466
[9] ON THE LIFTING OF HILBERT CUSP FORMS TO HILBERT-SIEGEL CUSP FORMS
Ikeda, Tamotsu
Yamana, Shunsuke
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 2020, 53 (05): : 1121 - 1181
[10] The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
Du Kim, Byoung
Park, Jeehoon
ACTA ARITHMETICA, 2017, 181 (03) : 209 - 238

← 1 2 3 4 5 →