Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes

被引:14
作者
Longo, Matteo [1 ]
Vigni, Stefano [2 ]
机构
[1] Univ Padua, Dipartimento Matemat, Via Trieste 63, I-35121 Padua, Italy
[2] Univ Genoa, Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy
来源
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA | 2019年 / 12卷 / 03期
关键词
Elliptic curves; Iwasawa theory; Supersingular primes; Heegner points; CONJECTURE; Z(P)-EXTENSIONS; VALUES;
D O I
10.1007/s40574-018-0162-4
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We extend to the supersingular case the Lambda-adic Euler system method (where Lambda is a suitable Iwasawa algebra) for Heegner points on elliptic curves that was originally developed by Bertolini in the ordinary setting. In particular, given an elliptic curve E over Q with supersingular reduction at a prime p >= 5, we prove results on the Lambda-corank of certain plus/minus p-primary Selmer groups a la Kobayashi of E over the anticyclotomic Z(p)-extension of an imaginary quadratic field and on the asymptotic behaviour of p-primary Selmer groups of E when the base field varies over the finite layers of such a Z(p)-extension. These theorems can be alternatively obtained by combining results of Nekovar, Vatsal and Iovita-Pollack, but do not seem to be directly available in the current literature.
引用
收藏
页码:315 / 347
页数:33
相关论文
共 38 条
  • [1] Agboola A, 2005, MATH RES LETT, V12, P611
  • [2] [Anonymous], 1986, GRADUATE TEXTS MATH
  • [3] Balister P. N., 1997, ASIAN J MATH, V1, P224, DOI DOI 10.4310/AJM.1997.V1.N2.A2
  • [4] BERTOLINI M, 1990, J REINE ANGEW MATH, V412, P63
  • [5] BERTOLINI M, 1995, COMPOS MATH, V99, P153
  • [6] Heegner points on Mumford-Tate curves
    Bertolini, M
    Darmon, H
    [J]. INVENTIONES MATHEMATICAE, 1996, 126 (03) : 413 - 456
  • [7] BERTOLINI M., 2001, 21 JOURNE ES ARITHME, V13, P1
  • [8] Brown K.S., 1982, GRADUATE TEXTS MATH, V87
  • [9] Solvable points on genus one curves
    Ciperiani, Mirela
    Wiles, Andrew
    [J]. DUKE MATHEMATICAL JOURNAL, 2008, 142 (03) : 381 - 464
  • [10] Tate-Shafarevich groups in anticyclotomic Zp-extensions at supersingular primes
    Ciperiani, Mirela
    [J]. COMPOSITIO MATHEMATICA, 2009, 145 (02) : 293 - 308