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

[21] Estimating the growth in Mordell–Weil ranks and Shafarevich–Tate groups over Lie extensions
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[22] Weil-Ch(a)over-captelet divisible elements in Tate-Shafarevich groups II: On a question of Cassels
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[23] The main conjecture of Iwasawa theory for elliptic curves with complex multiplication over abelian extensions at supersingular primes
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[25] A CLASSICAL FAMILY OF ELLIPTIC CURVES HAVING RANK ONE AND THE 2-PRIMARY PART OF THEIR TATE-SHAFAREVICH GROUP NON-TRIVIAL
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[28] The p-adic Gross-Zagier formula for elliptic curves at supersingular primes
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[29] Iwasawa invariants for elliptic curves over Zp -extensions and Kida's formula
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[30] SELMER GROUPS FOR ELLIPTIC CURVES IN Zld-EXTENSIONS OF FUNCTION FIELDS OF CHARACTERISTIC p
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