On arithmetic fundamental lemmas

• 成果类型: Article
• 署名作者: Zhang, Wei
• 署名单位: Harvard University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0348-1
• 发表日期: 2012
• 页码: 197-252
• 关键词: heegner points; derivatives; VALUES

摘要

We present a relative trace formula approach to the Gross-Zagier formula and its generalization to higher-dimensional unitary Shimura varieties. As a crucial ingredient, we formulate a conjectural arithmetic fundamental lemma for unitary Rapoport-Zink spaces. We prove the conjecture when the Rapoport-Zink space is associated to a unitary group in two or three variables.