On the anticyclotomic Iwasawa theory of rational elliptic curves at Eisenstein primes

被引：8

作者：

Castella, Francesc ^{[1
]}

Grossi, Giada ^{[2
]}

Lee, Jaehoon ^{[3
]}

Skinner, Christopher ^{[4
]}

机构：

[1] Univ Calif Santa Barbara, South Hall, Santa Barbara, CA 93106 USA

[2] Univ Sorbonne Paris Nord, Inst Galilee, F-93430 Villetaneuse, France

[3] Korea Adv Inst Sci & Technol, 291 Daehak Ro, Daejeon 34141, South Korea

[4] Princeton Univ, Fine Hall,Washington Rd, Princeton, NJ 08544 USA

来源：

INVENTIONES MATHEMATICAE | 2022年 / 227卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

ADIC L-FUNCTIONS; GENERALIZED HEEGNER CYCLES; SWINNERTON-DYER FORMULA; ABELIAN-VARIETIES; SELMER GROUPS; POINTS; ZAGIER; BIRCH; GROSS; CONJECTURES;

D O I：

10.1007/s00222-021-01072-y

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 an odd prime where E has good reduction, and assume that E admits a rational p-isogeny. In this paper we study the anticyclotomic Iwasawa theory of E over an imaginary quadratic field in which p splits, which we relate to the anticyclotomic Iwasawa theory of characters by a variation of the method of Greenberg-Vatsal. As a result of our study we obtain proofs (under relatively mild hypotheses) of PerrinRiou's Heegner point main conjecture, a p-converse to the theorem of GrossZagier and Kolyvagin, and the p-part of the Birch-Swinnerton-Dyer formula in analytic rank 1, for Eisenstein primes p.

引用

页码：517 / 580

页数：64

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