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Compactifications of subschemes of integral models of Hodge-type Shimura

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

毛盛开

时间

2024年12月02日 10:00 至 11:00

地点

Shuangqing-C654

摘要

The special fiber of the integral model of a Hodge-type Shimura variety with parahoric level structure admits stratifications that capture various geometric aspects of the universal abelian scheme. A detailed study of these strata provides valuable insights into the cohomological properties of Shimura varieties. On the other hand, the compactification theory for integral models allows us to define partial compactifications of these strata at the boundary. In this talk, we will explain the boundary behavior of these strata, including central leaves, Igusa varieties, Newton strata, Kottwitz-Rapoport strata, and Ekedahl-Kottwitz-Oort-Rapoport strata. We will also provide some geometric and cohomological applications of these results. This work builds upon and generalizes some previous work by Kai-Wen Lan and Benoît Stroh.