On the Hodge–Newton Filtration for p-Divisible Groups with Additional Structures

We prove that, for a p-divisible group with additional structures over a complete valuation ring of rank 1 OK with mixed characteristic (0,p), if the Newton polygon and the Hodge polygon of its special fiber possess a nontrivial contact point, which is a break point for the Newton polygon, then it admits of a “Hodge–Newton filtration” over OK. The proof is based on the theories of Harder–Narasimhan filtration of finite flat group schemes and admissible filtered isocrystals. We then apply this result to the study of some larger class of Rapoport–Zink spaces and Shimura varieties than those in [26], and confirm some new cases Harris’s Conjecture 5.2 of [16].