Kudla program for unitary Shimura varieties

Abstract

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.