Igusa Stack for some expectional Shimura Varieties

Abstract: We study the integral models of meta-unitary Shimura varieties through the lens of Scholze's fiber product conjecture. Reformulating Bultel's original construction in terms of moduli stacks of Shtukas and Igusa stacks, we prove the validity of the fiber product formula for this class of non-abelian type Shimura varieties, thereby generalizing the works of Zhang and Daniels, Van Hoften, Kim, and Zhang. We utilize this geometric description to derive local-global compatibility results and, adapting the strategy of Zhu and Yang, apply the unipotent categorical local Langlands correspondence to prove a general vanishing theorem for the generic part of the cohomology of meta-unitary Shimura varieties.