Boundary structures of integral models of Hodge-type Shimura Varieties
Shengkai Mao
TL;DR
The paper analyzes boundary structures of integral models for Shimura varieties of Hodge type with quasi-parahoric levels. It develops a comprehensive framework for boundary level groups, unifies Levi, unipotent, and toral data via Bruhat-Tits and Yu’s open-cell methods, and proves that boundary strata are finite quotients of smaller mixed Shimura models. It then establishes that minimal and toroidal compactifications are independent of Siegel embeddings in this setting and constructs canonical change-of-parahoric morphisms between integral models, compatible with boundary stratifications. Collectively, these results provide a precise, functorial picture of boundary behavior in both local and global (adelic) contexts, with implications for the modular interpretation of boundary strata and for the structure of integral models across varying level structures.
Abstract
We compute the level groups associated with mixed Shimura varieties that appear at the boundaries of compactifications of Shimura varieties and show that the boundaries of minimal compactifications of Pappas-Rapoport integral models are finite quotients of smaller Pappas-Rapoport integral models. Additionally, we prove that the compactifications of integral models of Hodge-type Shimura varieties with quasi-parahoric level structures are independent of the choice of Siegel embedding, and use this to construct and analyze the change-of-parahoric morphisms on these compactifications.