Stark-Heegner cycles attached to Bianchi modular forms

doi:10.1112/jlms.12438

	Stark-Heegner cycles attached to Bianchi modular forms
	Venkat, Guhan 2; Williams, Chris 1
刊名	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
	2021-01-20
页码	29
ISSN号	0024-6107
DOI	10.1112/jlms.12438
英文摘要	Let f be a Bianchi modular form, that is, an automorphic form for GL(2) over an imaginary quadratic field F, and let p be a prime of F at which f is new. Let K be a quadratic extension of F, and L(f/K,s) the L-function of the base-change of f to K. Under certain hypotheses on f and K, the functional equation of L(f/K,s) ensures that it vanishes at the central point. The Bloch-Kato conjecture predicts that this should force the existence of non-trivial classes in an appropriate global Selmer group attached to f and K. In this paper, we use the theory of double integrals developed by Salazar and the second author to construct certain p-adic Abel-Jacobi maps, which we use to propose a construction of such classes via Stark-Heegner cycles. This builds on ideas of Darmon and in particular generalises an approach of Rotger and Seveso in the setting of classical modular forms.
资助项目	NSERC[05710] ; CRM-Laval postdoctoral fellowship ; Heilbronn research fellowship
WOS研究方向	Mathematics
语种	英语
出版者	WILEY
WOS记录号	WOS:000608974600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58027]
专题	中国科学院数学与系统科学研究院
通讯作者	Venkat, Guhan
作者单位	1.Univ Warwick, Math Inst, Zeeman Bldg, Coventry CV4 7AL, W Midlands, England 2.Chinese Acad Sci, Acad Math & Syst Sci, Morningside Ctr Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Venkat, Guhan,Williams, Chris. Stark-Heegner cycles attached to Bianchi modular forms[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,2021:29.
APA	Venkat, Guhan,&Williams, Chris.(2021).Stark-Heegner cycles attached to Bianchi modular forms.JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,29.
MLA	Venkat, Guhan,et al."Stark-Heegner cycles attached to Bianchi modular forms".JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (2021):29.