2025/05/14 by Peiling Wu, Wu, Peihang
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems
paper · pdf · doi:10.48550/arxiv.2505.09135
In this paper, we construct good toroidal and minimal compactifications in the sense of Lan-Stroh for integral models of abelian-type Shimura varieties. We start with finding suitable types of cusp labels and cone decompositions which are compatible with those of the associated Hodge-type Shimura varieties. We then study the action of ℚ-points of the adjoint group on boundary charts and toroidal compactifications of Hodge-type integral models. In particular, we extend the twisting construction of Kisin and Pappas to boundary charts. Finally, up to taking refinements of cone decompositions, we construct an abelian-type toroidal compactification as an open and closed algebraic subspace of a quotient from a disjoint union of Hodge-type toroidal compactifications and construct minimal compactifications with a similar method. Furthermore, we show results on nearby cycles of these compactifications and verify Pink's formula when the level at p is an intersection of n quasi-parahoric subgroups.