Shtukas and the Taylor expansion of L-functions

• 成果类型: Article
• 署名作者: Yun, Zhiwei; Zhang, Wei
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2017.186.3.2
• 发表日期: 2017
• 页码: 767-911
• 关键词: intersection theory; fundamental lemma; algebraic stacks; artin stacks

摘要

We define the Heegner Drinfeld cycle on the moduli stack of Drinfeld Shtukas of rank two with r-modifications for an even integer r. We prove an identity between (1) the r-th central derivative of the quadratic base change L-function associated to an everywhere unramified cuspidal automorphic representation pi of PGL(2), and (2) the self-intersection number of the pi-isotypic component of the Heegner Drinfeld cycle. This identity can be viewed as a function-field analog of the Waldspurger and Gross-Zagier formula for higher derivatives of L-functions.