Abstract

In this talk, we study the special fiber of U(2r, 1) Shimura varieties at an inert prime. We exhibitelements in the higher Chow group of the supersingular locus and use this to prove the surjectivityof the arithmetic level-raising map. A key ingredient of the proof is to show a form of lharas lemmafor odd definite unitary groups. The proof relies heavily on the description of supersingular locusand 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 asan even-dimensional analogue of the ongoing work of Yifeng Liu, Yichao Tian, and Liang Xiao.

(This talk is on-site. There is no zoom available for this talk.)