酉志村簇的Kudla纲领

Kudla program for unitary Shimura varieties

本文首先回顾和总结关于酉志村簇的Kudla纲领的最新研究进展.本文展示局部算术Siegel-Weil公式如何推导出U(n, 1)的非退化系数整体算术Siegel-Weil公式.特别地,本文证明U(1, 1)的非退化系数整体算术Siegel-Weil公式.

In this paper, we first review and summarize some recent progress in Kudla program on unitary Shimura varieties. We show how the local arithmetic Siegel-Weil formula implies the global arithmetic Siegel-Weil formula for non-singular coefficients on U(n, 1). In particular, the arithmetic Siegel-Weil formula for non-singular coefficients on U(1, 1) is true.