We study the geometry of reduction modulo p of the Kisin-Pappas integral models for certain Shimura varieties of abelian type with parahoric level structure. We give some direct and geometric constructions for the EKOR (Ekedahl–Kottwitz–Oort–Rapoport) strata on these Shimura varieties, using the theories of G-zips and mixed characteristic local G-Shtukas. We establish several basic properties of these strata, including the smoothness, dimension formula, and closure relation. Moreover, we apply our results to the study of Newton strata and central leaves on these Shimura varieties.

Publication:

-    Duke Mathematical Journal, (2021)

Authors:

-    Xu Shen (Morningside Center of Mathematics, AMSS, Chinese Academy of Sciences)

-    Chia-Fu Yu (Institute of Mathematics, Academia Sinica and NCTS)

-    Chao Zhang (Shing-Tung Yau Center of Southeast University)