Green forms and the arithmetic Siegel-Weil formula

• 成果类型: Article
• 署名作者: Garcia, Luis E.; Sankaran, Siddarth
• 署名单位: University of Toronto; University of Manitoba
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0839-4
• 发表日期: 2019
• 页码: 863-975
• 关键词: series

摘要

We construct natural Green forms for special cycles in orthogonal and unitary Shimura varieties, in all codimensions, and, for compact Shimura varieties of type O(p,2) and U(p,1), we show that the resulting local archimedean height pairings are related to special values of derivatives of Siegel Eisentein series. A conjecture put forward by Kudla relates these derivatives to arithmetic intersections of special cycles, and our results settle the part of his conjecture involving local archimedean heights.