Modular heights of unitary Shimura varieties

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Ziqi Guo (Peking University)

Time：

Mon., 10:00- 11:00 am, Nov. 3, 2025

Venue：

B627, Shuangqing Complex Building A

Title:

Modular heights of unitary Shimura varieties

Abstract:

The goal of our work is to prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithm derivative of the Hecke L-function associated with the CM extension. In a more specific term, we will introduce a global canonical integral model of such a unitary Shimura variety, and compute the arithmetic top self-intersection number of a canonical arithmetic line bundle with Hermitian metric on such integral model. At the same time, we also delve into a thorough investigation of the arithmetic generating series of divisors on unitary Shimura varieties. Therefore, we will also obtain the so-called “arithmetic Siegel-Weil formula” in our setting.