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Splitting models for unitary Shimura varieties of maximal parahoric level

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

石友晟

时间

2025年06月05日 10:00 至 11:00

地点

Shuangqing-C654

摘要

I will first briefly review the theory of integral models of Shimura varieties. Then I will discuss a semi-stable model for unitary Shimura varieties of signature $(n-1,1)$ with maximal parahoric level structure at ramified primes using the idea of splitting models first developed by Pappas and Rapoport. In this case, the "naive" splitting model defined by Pappas and Rapoport fails to be flat in a crucial way. We prove that the genuine splitting model in this case is flat with semi-stable reduction. As an application, I will show that in this case certain automorphic vector bundles extend from the generic fiber to the splitting model, but not to the canonical integral model. This talk is based on a joint work with Qiao He and Yu Luo.