The conjecture of Birch and Swinnerton-Dyer for certain elliptic curves with complex multiplication

被引：0

作者：

Burungale, Ashay ^{[1
,2
]}

Flach, Matthias ^{[3
]}

机构：

[1] CALTECH, Dept Math 258, Pasadena, CA 91125 USA

[2] Univ Texas Austin, Austin, TX 78712 USA

[3] CALTECH, Dept Math 253 37, Pasadena, CA 91125 USA

来源：

CAMBRIDGE JOURNAL OF MATHEMATICS | 2024年 / 12卷 / 02期

关键词：

Elliptic curves; Birch and Swinnerton-Dyer Conjecture; Complex multiplication; CENTRAL L-VALUES; CANONICAL HECKE CHARACTERS; EXPLICIT GROSS-ZAGIER; 2ND LOWEST 2-POWER; IWASAWA THEORY; QUADRATIC TWISTS; MAIN CONJECTURE; CONGRUENT NUMBERS; CRITERION; VALUATIONS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E/F be an elliptic curve over a number field F with complex multiplication by the ring of integers in an imaginary quadratic field K. We give a complete proof of the conjecture of Birch and Swinnerton-Dyer for E/F, as well as its equivariant refinement formulated by Gross [39], under the assumption that L(E/F, 1) not equal 0 and that F(E-tors)/K is abelian. We also prove analogous results for CM abelian varieties A/K.

引用

页码：357 / 415

页数：59

共 50 条

[1] Elliptic curves with complex multiplication and the conjecture of birch and Swinnerton-Dyer
Rubin, K
ARITHMETIC THEORY OF ELLIPTIC CURVES, 1999, 1716 : 167 - 234
[2] ELLIPTIC-CURVES WITH COMPLEX MULTIPLICATION AND THE CONJECTURE OF BIRCH AND SWINNERTON-DYER
RUBIN, K
INVENTIONES MATHEMATICAE, 1981, 64 (03) : 455 - 470
[3] COMPUTATIONAL VERIFICATION OF THE BIRCH AND SWINNERTON-DYER CONJECTURE FOR INDIVIDUAL ELLIPTIC CURVES
Grigorov, Grigor
Jorza, Andrei
Patrikis, Stefan
Stein, William A.
Tarnita, Corina
MATHEMATICS OF COMPUTATION, 2009, 78 (268) : 2397 - 2425
[4] Generalized Birch lemma and the 2-part of the Birch and Swinnerton-Dyer conjecture for certain elliptic curves
Shu, Jie
Zhai, Shuai
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2021, 775 : 117 - 143
[5] Elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture mod 3
James, K
JOURNAL OF NUMBER THEORY, 1999, 76 (01) : 16 - 21
[6] CONJECTURE OF BIRCH AND SWINNERTON-DYER
COATES, J
WILES, A
INVENTIONES MATHEMATICAE, 1977, 39 (03) : 223 - 251
[7] ON THE BIRCH AND SWINNERTON-DYER CONJECTURE
GREENBERG, R
INVENTIONES MATHEMATICAE, 1983, 72 (02) : 241 - 265
[8] On the Birch and Swinnerton-Dyer conjecture
Virdol, Cristian
ACTA ARITHMETICA, 2011, 146 (02) : 173 - 176
[9] On a conjecture of Birch and Swinnerton-Dyer
Kuo, WT
Murty, MR
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2005, 57 (02): : 328 - 337
[10] On the conjecture of Birch and Swinnerton-Dyer
GonzalezAviles, CD
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (10) : 4181 - 4200

← 1 2 3 4 5 →