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

被引:15
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
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