On the Hodge-Newton filtration for p-divisible groups with additional structures

TL;DR

This paper establishes a Hodge-Newton filtration for p-divisible groups with additional structures over valuation rings, linking Newton and Hodge polygons, and applies it to Rapoport-Zink spaces and Shimura varieties.

Contribution

It proves the existence of Hodge-Newton filtrations under specific conditions and extends applications to broader classes of Rapoport-Zink spaces and Shimura varieties.

Findings

Hodge-Newton filtration exists when polygons have a contact point at a break point.

Application to larger classes of Rapoport-Zink spaces and Shimura varieties.

Confirmation of new cases of Harris's conjecture.

Abstract

We prove that, for a $p$-divisible group with additional structures over a complete valuation ring of rank one $O_K$ with mixed characteristic $(0,p)$, if the Newton polygon and the Hodge polygon of its special fiber possess a non trivial contact point, which is a break point for the Newton polygon, then it admits a "Hodge-Newton filtration" over $O_K$. 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 studied previously by Mantovan, and confirm some new cases of Harris's conjecture.