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BIMSA-YMSC Tsinghua Number Theory Seminar | Arithmetic Level Raising for U(2r, 1)

Time:Mon.,10:00-11:00 am, Apr. 1, 2024

Venue:B627, Shuangqing Complex Building A 清华大学双清综合楼A座 B627

Organizer:Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu, Yihang Zhu

Speaker:Ruiqi Bai (PKU)

Abstract:

In this talk, we study the special fiber of U(2r, 1) Shimura varieties at an inert prime. We exhibit elements in the higher Chow group of the supersingular locus and use this to prove the surjectivity of the arithmetic level-raising map. A key ingredient of the proof is to show a form of Ihara’s lemma for odd definite unitary groups. The proof relies heavily on the description of supersingular locus and EKOR stratification on the special fibers with parahoric levels. This is a joint work with Hao Fu. It is inspired by the work of Rong Zhou on quaternionic Shimura varieties, and it can be viewed as an even-dimensional analogue of the ongoing work of Yifeng Liu, Yichao Tian, and Liang Xiao.

DATEMarch 31, 2024
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