BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

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

Speaker：

Xiaojiang Cheng (YMSC)

Time：

Mon., 10:00-11:00 am, Oct. 21, 2024

Venue：

C654, Shuangqing Complex Building （新增线上ZOOM，详情见文末评论区）

Title：

Hodge Classes in the Cohomology of Local Systems

Abstract:

Let S be an arithmetic quotient of a Hermitian symmetric domain and X/S be a family of varieties over S. One interesting problem is to find the Hodge classes of X, and if possible, to prove the Hodge conjecture for X. In this talk, I will explain my recent work on the Hodge conjecture for certain families of varieties over arithmetic quotients of balls and the Siegel domain of degree two. In particular, we recovered Arapura’s result for genus two modular fourfolds. We have applied techniques of automorphic forms and derived formulas for Hodge numbers of cohomology of local systems in terms of automorphic forms.