On Ihara's lemma for definite unitary groups

Clozel, Harris and Taylor proposed a generalized Ihara's lemma for definite unitary groups. In this talk, we prove some cases of their conjecture under the assumption of banal coefficients. The proof relies on the recent work of Hemo and Zhu on unipotent categorical local Langlands correspondence, and the construction of Igusa stacks by Daniels, van Hoften, Kim and Zhang.