Venue: Lecture Hall of IASM, ZJU

Time: 16:00-17:00, June 4

Speaker: 杨向谦 Xiangqian Yang (Peking University)

Abstract: 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. A key ingredient in the proof is a local-global compatibility result for the cohomology of Shimura varieties, formulated in terms of coherent sheaves on the moduli stack of local Langlands parameters. This result is based on the unipotent categorical local Langlands correspondence recently established by Zhu, and the construction of Igusa stacks by Daniels, van Hoften, Kim, and Zhang.