Heegner Points over Towers of Kummer Extensions

doi:10.4153/CJM-2010-039-8

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	Heegner Points over Towers of Kummer Extensions
	Darmon, Henri 1; Tian, Ye2
	2010-10-01
发表期刊	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN	0008-414X
卷号	62 期号:5 页码:1060-1081
摘要	Let E be an elliptic curve, and let L(n) be the Kummer extension generated by a primitive p(n)-th root of unity and a p(n)-th root of a for a fixed a is an element of Q(x) - {+/- 1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over L(n) in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.
DOI	10.4153/CJM-2010-039-8
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000282246500007
出版者	CANADIAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10118
专题	数学所
通讯作者	Darmon, Henri
作者单位	1.McGill Univ, Dept Math, Montreal, PQ H3A 2T5, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Darmon, Henri,Tian, Ye. Heegner Points over Towers of Kummer Extensions[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2010,62(5):1060-1081.
APA	Darmon, Henri,&Tian, Ye.(2010).Heegner Points over Towers of Kummer Extensions.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,62(5),1060-1081.
MLA	Darmon, Henri,et al."Heegner Points over Towers of Kummer Extensions".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 62.5(2010):1060-1081.