Title: Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure,
Abstract: We study the special fiber of the integral models for Shimura varieties of
Hodge type with parahoric level structure constructed by Kisin and Pappas in
[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 [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.