Compactifications of subschemes of integral models of Hodge-type Shimura varieties

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu

Speaker：

Shengkai Mao (MCM)

Time：

Mon., 10:00-11:00 am, Dec. 2, 2024

Venue：

C654, Shuangqing Complex Building A

Title：

Compactifications of subschemes of integral models of Hodge-type Shimura varieties

Abstract：

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.