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

• 成果类型: Article
• 署名作者: Castella, Francesc; Grossi, Giada; Lee, Jaehoon; Skinner, Christopher
• 署名单位: University of California System; University of California Santa Barbara; Korea Advanced Institute of Science & Technology (KAIST); Princeton University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01072-y
• 发表日期: 2022
• 页码: 517-580
• 关键词: adic l-functions; generalized heegner cycles; swinnerton-dyer formula; abelian-varieties; selmer groups; points; zagier; birch; gross; conjectures

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.