Hodge–Newton filtration for $p$-divisible groups with ramified endomorphism structure

Abstract

Let O K be a complete discrete valuation ring of mixed characteristic (0, p) with perfect residue field. We prove the existence of the Hodge-Newton filtration for p-divisible groups over O K with additional endomorphism structure for the ring of integers of a finite, possibly ramified field extension of Q p . The argument is based on the Harder-Narasimhan theory for finite flat group schemes over O K . In particular, we describe a sufficient condition for the existence of a filtration of p-divisible groups over O K associated to a break point of the Harder-Narasimhan polygon. 2020 Mathematics Subject Classification: 14L05 Keywords and Phrases: p-divisible groups, Hodge-Newton filtration, Harder-Narasimhan theory, ramified PEL structure Contents A. Marrama 3 p-divisible groups 1825 3.1 p-divisible groups with endomorphism structure .