p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin

doi:10.1007/s00222-019-00929-7

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	p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin
	Burungale, Ashay A.1; Tian, Ye 2,3
	2019-11-02
发表期刊	INVENTIONES MATHEMATICAE
ISSN	0020-9910
页码	43
摘要	Let E be a CM elliptic curve over the rationals and p>3-Selmer group Selp infinity(E/Q) and the complex L-function L(s,E/Q). In particular, the Tate-Shafarevich group X(E/Q) is finite whenever corankZpSelp infinity(E/Q)=1. We also prove an analogous p-converse for CM abelian varieties arising from weight two elliptic CM modular forms with trivial central character. For non-CM elliptic curves over the rationals, first general results towards such a p-converse theorem are independently due to Skinner (A converse to a theorem of Gross, Zagier and Kolyvagin, , 2014) and Zhang (Camb J Math 2(2):191-253, 2014).
DOI	10.1007/s00222-019-00929-7
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000493674500001
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/50700
专题	中国科学院数学与系统科学研究院
通讯作者	Burungale, Ashay A.
作者单位	1.CALTECH, 1200 E Calif Blvd, Pasadena, CA 91125 USA 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, HLM, MCM, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Burungale, Ashay A.,Tian, Ye. p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin[J]. INVENTIONES MATHEMATICAE,2019:43.
APA	Burungale, Ashay A.,&Tian, Ye.(2019).p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin.INVENTIONES MATHEMATICAE,43.
MLA	Burungale, Ashay A.,et al."p-converse to a theorem of Gross-Zagier, Kolyvagin and Rubin".INVENTIONES MATHEMATICAE (2019):43.