Iwasawa main conjecture for Rankin-Selberg p-adic L-functions

doi:10.2140/ant.2020.14.383

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	Iwasawa main conjecture for Rankin-Selberg p-adic L-functions
	Wan, Xin 1,2
	2020
发表期刊	ALGEBRA & NUMBER THEORY
ISSN	1937-0652
卷号	14 期号:2 页码:383-483
摘要	In this paper we prove that the p-adic L-function that interpolates the Rankin-Selberg product of a general modular form and a CM form of higher weight divides the characteristic ideal of the corresponding Selmer group. This is one divisibility of the Iwasawa main conjecture for this p-adic L-function. We prove this conjecture using congruences between Klingen-Eisenstein series and cusp forms on the group GU(3, 1), following the strategy of recent work by C. Skinner and E. Urban. The actual argument is, however, more complicated due to the need to work with general Fourier-Jacobi expansions. This theorem is used to deduce a converse of the Gross-Zagier-Kolyvagin theorem and the p-adic part of the precise BSD formula in the rank one case.
关键词	Iwasawa main conjecture Rankin-Selberg
DOI	10.2140/ant.2020.14.383
收录类别	SCI
语种	英语
资助项目	Chinese Academy of Science[Y729025EE1] ; NSFC[11688101] ; NSFC[11621061]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000537944500004
出版者	MATHEMATICAL SCIENCE PUBL
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51588
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, Peoples R China 2.Univ Chinese Acad Sci, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Wan, Xin. Iwasawa main conjecture for Rankin-Selberg p-adic L-functions[J]. ALGEBRA & NUMBER THEORY,2020,14(2):383-483.
APA	Wan, Xin.(2020).Iwasawa main conjecture for Rankin-Selberg p-adic L-functions.ALGEBRA & NUMBER THEORY,14(2),383-483.
MLA	Wan, Xin."Iwasawa main conjecture for Rankin-Selberg p-adic L-functions".ALGEBRA & NUMBER THEORY 14.2(2020):383-483.