BIMSA > BIMSA-YMSC Tsinghua Number Theory Seminar Modular heights of unitary Shimura varieties
Modular heights of unitary Shimura varieties
Organizers
Hansheng Diao , Heng Du , Yueke Hu , Bin Xu , Yihang Zhu
Speaker
Ziqi Guo
Time
Monday, November 3, 2025 10:00 AM - 11:00 AM
Venue
Shuangqing-B627
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.