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

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

2012-03-12

arxiv.org/abs/1203.2541v1

Mathematics

Number Theory

34 pages

Scientific paper

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 in Mantovan, and confirm some new cases of Harris's conjecture 5.2 in Harris.

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