Time： September 11, Wednesday, 16:00-17:00

Venue: Lecture Hall

Speacker: Ruiqi Bai ( University of Cambridge )

Abstract: I will talk about the ongoing work with Hao Fu to show an arithmetic level-raising result ffor the special fiber of U(2r, 1) Shimura variety 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 Abel–Jacobi map. A key ingredient of the proof is to show a form of Ihara’s lemma. This work 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. We would like to express our sincere gratitude to IASM for the assistance provided during our visit in 2022.