Following the foundational work of Fargues--Scholze, the categorical local Langlands correspondence was recently proven by Hansen--Mann for many classical groups. A natural question is to understand how it interacts with global Langlands, namely the cohomology of Shimura varieties. The main geometric input for answering such questions is the Igusa stack, an object constructed by Zhang in 2023 for PEL type Shimura varieties and extended to all abelian type cases in joint work with Daniels, van Hoften, and Zhang. I will discuss how arguments of Koshikawa can be used to prove strong local-global compatibility statements.

---

카이스트 동문 김동률 박사와 동명이인입니다.