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

2012/03/12 by Xu Shen, Shen, Xu
Mathematics · #14G35 #14L05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #math.NT #msc:14G35 #msc:14L05

paper · pdf · doi:10.48550/arxiv.1203.2541

34 pages, add a reference; grammar errors are corrected; a slightly short version will appear in International Mathematics Research Notices

openalex publication_date 2012/03/12 · arxiv created 2013/02/20 · arxiv updated 2013/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Compactly supported cohomology and nearby cycle cohomology of open Shimura varieties of PEL type

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