Modular Heights of Unitary Shimura Varieties

Time：Monday, 10:00- 11:00 am Nov. 3, 2025

Venue：B627 Shuangqing Complex Building A

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

Speaker： Ziqi Guo

Modular Heights of

Unitary Shimura Varieties

Organizers

Hansheng Diao, Heng Du, Yueke Hu,

Bin Xu, Yihang Zhu

Speaker

Ziqi Guo (Peking University)

Time

Monday, 10:00- 11:00 am

Nov. 3, 2025

Venue

B627

Shuangqing Complex Building A

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.

DATEOctober 31, 2025

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