Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure
  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.
