Kisin, MarkZhou, Rong2019-05-202017-052017-05-112017http://nrs.harvard.edu/urn-3:HUL.InstRepos:40046516We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in \cite{KP}. We show that when the group is residually split, the points in the mod $p$ isogeny classes have the form predicted by the Langlands Rapoport conjecture in \cite{LR}. We also verify most of the He-Rapoport axioms for these integral models without the residually split assumption. This allows us to prove that all Newton strata are non-empty for these models.application/pdfenMathematicsThesis or Dissertation2019-05-20