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

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