Heegner Point Kolyvagin System and Iwasawa Main Conjecture

doi:10.1007/s10114-021-8355-7

	Heegner Point Kolyvagin System and Iwasawa Main Conjecture
	Wan, Xin 1,2
刊名	ACTA MATHEMATICA SINICA-ENGLISH SERIES
	2021
卷号	37 期号:1 页码:104-120
关键词	Iwasawa theory Heegner Kolyvagin
ISSN号	1439-8516
DOI	10.1007/s10114-021-8355-7
英文摘要	We prove an anticyclotomic Iwasawa main conjecture proposed by Perrin-Riou for Heegner points for semi-stable elliptic curves E over a quadratic imaginary field K satisfying a certain generalized Heegner hypothesis, at an ordinary prime p. It states that the square of the index of the anticyclotomic family of Heegner points in E equals the characteristic ideal of the torsion part of its Bloch-Kato Selmer group (see Theorem 1.3 for precise statement). As a byproduct we also prove the equality in the Greenberg-Iwasawa main conjecture for certain Rankin-Selberg product (Theorem 1.7) under some local conditions, and an improvement of Skinner's result on a converse of Gross-Zagier and Kolyvagin theorem (Corollary 1.11).
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000610528800006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58073]
专题	中国科学院数学与系统科学研究院
通讯作者	Wan, Xin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Wan, Xin. Heegner Point Kolyvagin System and Iwasawa Main Conjecture[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2021,37(1):104-120.
APA	Wan, Xin.(2021).Heegner Point Kolyvagin System and Iwasawa Main Conjecture.ACTA MATHEMATICA SINICA-ENGLISH SERIES,37(1),104-120.
MLA	Wan, Xin."Heegner Point Kolyvagin System and Iwasawa Main Conjecture".ACTA MATHEMATICA SINICA-ENGLISH SERIES 37.1(2021):104-120.