Wu, Peihang2025-01-282025-01-282024-08https://hdl.handle.net/11299/269662University of Minnesota Ph.D. dissertation. August 2024. Major: Mathematics. Advisor: Kai-Wen Lan. 1 computer file (PDF); iii, 173 pages.We construct toroidal compactifications of integral models of abelian-type Shimura varieties when the Shimura datum G₂, X₂ satisfies the assumptions in [Kis10] or [KP15], and when the level at 𝑝 is contained in a hyperspecial or a parahoric subgroup. First, we find suitable types of cusp labels and cone decompositions which are compatible with those of toroidal compactifications of associated Hodge-type Shimura varieties. Then, we extend the twisting actions considered in [Kis10] and [KP15] on integral models of Hodge-type Shimura varieties to their toroidal compactifications. Finally, we construct toroidal compactifications up to refinements of given cone decompositions in a suitable cofinal family of cone decompositions, which admits smooth and projective refinements in itself.enThesis or Dissertation