Asymptotic formula for Tate-Shafarevich groups of p-supersingular elliptic curves over anticyclotomic extensions

被引：1

作者：

Lei, Antonio ^{[1
]}

Lim, Meng Fai ^{[2
,3
]}

Mueller, Katharina ^{[4
]}

机构：

[1] Univ Ottawa, Dept Math & Stat, 150 Louis Pasteur Pvt, Ottawa, ON K1N 6N5, Canada

[2] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China

[3] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China

[4] Univ Laval, Dept Math & Stat, Pavill Alexandre Vachon,1045 Ave Med, Quebec City, PQ G1V 0A6, Canada

来源：

ADVANCES IN MATHEMATICS | 2023年 / 434卷

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

Anticyclotomic Iwasawa theory; Elliptic curves; Supersingular primes; Tate-Shafarevich groups; IWASAWA THEORY; HEEGNER CYCLES; SPECIAL VALUES; POINTS; Z(P)-EXTENSIONS; THEOREM;

D O I：

10.1016/j.aim.2023.109320

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p >= 5 be a prime number and E/Q an elliptic curve with good supersingular reduction at p. Under the generalized Heegner hypothesis, we investigate the p-primary subgroups of the Tate-Shafarevich groups of E over number fields contained inside the anticyclotomic Z(p)-extension of an imaginary quadratic field where p splits. (c) 2023 Elsevier Inc. All rights reserved.

引用

页数：28

共 33 条

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Ciperiani, Mirela
COMPOSITIO MATHEMATICA, 2009, 145 (02) : 293 - 308
[2] ON THE p-PRIMARY PART OF TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER Q WHEN p IS SUPERSINGULAR
Kim, Dohyeong
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 50 (02) : 407 - 416
[3] Mordell-Weil ranks and Tate-Shafarevich groups of elliptic curves with mixed-reduction type over cyclotomic extensions
Lei, Antonio
Lim, Meng Fai
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2022, 18 (02) : 303 - 330
[4] ON THE TATE-SHAFAREVICH GROUP OF ELLIPTIC CURVES OVER Q
Kim, Dohyeong
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (01) : 155 - 163
[5] Structure of Tate-Shafarevich groups of elliptic curves over global function fields
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MATHEMATISCHE ZEITSCHRIFT, 2024, 307 (03)
[7] ORDERS OF TATE-SHAFAREVICH GROUPS FOR THE NEUMANN-SETZER TYPE ELLIPTIC CURVES
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Szymaszkiewicz, Lucjan
MATHEMATICS OF COMPUTATION, 2018, 87 (311) : 1509 - 1522
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Coates, J.
Liang, Z.
Sujatha, R.
JOURNAL OF ALGEBRA, 2009, 322 (03) : 657 - 674
[9] ELLIPTIC CURVES WITH EXCEPTIONALLY LARGE ANALYTIC ORDER OF THE TATE-SHAFAREVICH GROUPS
Dabrowski, Andrzej
Szymaszkiewicz, Lucjan
COLLOQUIUM MATHEMATICUM, 2021, 166 (02) : 217 - 225
[10] The growth of Tate-Shafarevich groups in cyclic extensions
Ouyang, Yi
Xie, Jianfeng
COMPOSITIO MATHEMATICA, 2022, 158 (10) : 2014 - 2032

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