Mao, Shengkai2024-08-222024-08-222024-04https://hdl.handle.net/11299/265148University of Minnesota Ph.D. dissertation. April 2024. Major: Mathematics. Advisor: Kai-wen Lan. 1 computer file (PDF); ii, 237 pages.We prove that central leaves, Igusa varieties, Newton strata, Kottwitz-Rapoport Strata, Ekedahl-Kottwitz-Oort-Rapoport strata on the special fiber of a Kisin-Pappas integral model of a Hodge-type Shimura variety with parahoric level structure are well-positioned, generalizing the work of Lan and Stroh.enThesis or Dissertation