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.