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.

48 pages

References in corpus (1)

• Introduction to Shimura varieties with bad reduction of parahoric type

Cited by in corpus (2)

• The connected components of affine Deligne--Lusztig varieties
• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)