Integration on Hp x H and arithmetic applications

• 成果类型: Article
• 署名作者: Darmon, H
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.2307/3062142
• 发表日期: 2001
• 页码: 589-639
• 关键词: adic l-functions; heegner points; elliptic-curves; swinnerton-dyer; periods; uniformization; conjectures; birch

摘要

This article describes a conjectural p-adic analytic construction of global points on (modular) elliptic curves, points which are defined over the ring class fields of real quadratic fields. The resulting conjectures suggest that the classical Heegner point construction, and the theory of complex multiplication on which it is based, should extend to a variety of contexts in which the underlying field is not a CM field.