Supersingular elliptic curves over DOUBLE-STRUCK CAPITAL Z??-extensions

被引：1

作者：

Ciperiani, Mirela ^{[1
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2023年 / 2023卷 / 801期

关键词：

IWASAWA THEORY; LOCAL UNITS; POINTS; Z(P)-EXTENSIONS; CONJECTURE;

D O I：

10.1515/crelle-2023-0029

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E/Q be an elliptic curve and p a prime of supersingular reduction for E. Consider a quadratic extension L/Qp and the corresponding anticyclotomic Zp-extension L-8/L. We analyze the structure of the points E(L00)and describe two global implications of our results.

引用

页码：45 / 56

页数：12

共 21 条

[1] Arthur J., 1989, Annals of Math. Studies, V120
[2] On the modularity of elliptic curves over Q: Wild 3-adic exercises
Breuil, C
Conrad, B
Diamond, F
Taylor, R
[J]. JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 14 (04) : 843 - 939
[3] Burungale A., IN PRESS
[4] Rubin's conjecture on local units in the anticyclotomic tower at inert primes
Burungale, Ashay A.
Kobayashi, Shinichi
Ota, Kazuto
[J]. ANNALS OF MATHEMATICS, 2021, 194 (03) : 943 - 966
[5] Solvable points on genus one curves
Ciperiani, Mirela
Wiles, Andrew
[J]. DUKE MATHEMATICAL JOURNAL, 2008, 142 (03) : 381 - 464
[6] Tate-Shafarevich groups in anticyclotomic Zp-extensions at supersingular primes
Ciperiani, Mirela
[J]. COMPOSITIO MATHEMATICA, 2009, 145 (02) : 293 - 308
[7] Mazur's conjecture on higher Heegner points
Cornut, C
[J]. INVENTIONES MATHEMATICAE, 2002, 148 (03) : 495 - 523
[8] NONVANISHING THEOREMS FOR AUTOMORPHIC L-FUNCTIONS ON GL(2)
FRIEDBERG, S
HOFFSTEIN, J
[J]. ANNALS OF MATHEMATICS, 1995, 142 (02) : 385 - 423
[9] GREENBERG R., 2001, IAS PARK CITY MATH S, P407
[10] Gross B. H., 1991, L FUNCTIONS ARITHMET, V153, P235

← 1 2 3 →