On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives

doi:10.1007/s00222-021-01088-4

	On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives
	Liu, Yifeng 3; Tian, Yichao 2; Xiao, Liang 1; Zhang, Wei 4; Zhu, Xinwen 5
刊名	INVENTIONES MATHEMATICAE
	2022-01-21
页码	269
ISSN号	0020-9910
DOI	10.1007/s00222-021-01088-4
英文摘要	In this article, we study the Beilinson-Bloch-Kato conjecture for motives associated to Rankin-Selberg products of conjugate self-dual automorphic representations, within the framework of the Gan-Gross-Prasad conjecture. We show that if the central critical value of the Rankin-Selberg L-function does not vanish, then the Bloch-Kato Selmer group with coefficients in a favorable field of the corresponding motive vanishes. We also show that if the class in the Bloch-Kato Selmer group constructed from a certain diagonal cycle does not vanish, which is conjecturally equivalent to the nonvanishing of the central critical first derivative of the Rankin-Selberg L-function, then the Bloch-Kato Selmer group is of rank one.
资助项目	American Institute of Mathematics ; NSF[DMS-1702019] ; NSF[DMS-1502147] ; NSF[DMS-1752703] ; NSF[DMS-1838118] ; NSF[DMS-1901642] ; NSF[DMS-1902239] ; Sloan Research Fellowship ; Simons Fellowship ; Chinese NSF[NSFC-12071004] ; Chinese Ministry of Education
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000745495400002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59892]
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Yifeng
作者单位	1.Peking Univ, Beijing Int Ctr Math Res, Beijing 100871, Peoples R China 2.Chinese Acad Sci, Morningside Ctr Math, AMSS, Beijing 100190, Peoples R China 3.Zhejiang Univ, Inst Adv Study Math, Hangzhou 310058, Peoples R China 4.MIT, Dept Math, Cambridge, MA 02139 USA 5.CALTECH, Div Phys Math & Astron, Pasadena, CA 91125 USA
推荐引用方式 GB/T 7714	Liu, Yifeng,Tian, Yichao,Xiao, Liang,et al. On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives[J]. INVENTIONES MATHEMATICAE,2022:269.
APA	Liu, Yifeng,Tian, Yichao,Xiao, Liang,Zhang, Wei,&Zhu, Xinwen.(2022).On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives.INVENTIONES MATHEMATICAE,269.
MLA	Liu, Yifeng,et al."On the Beilinson-Bloch-Kato conjecture for Rankin-Selberg motives".INVENTIONES MATHEMATICAE (2022):269.