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Published September 2010 | Submitted
Journal Article Open

On the Hodge–Newton filtration for p-divisible O-modules

Abstract

The notions Hodge–Newton decomposition and Hodge–Newton filtration for F-crystals are due to Katz and generalize Messing's result on the existence of the local-étale filtration for p-divisible groups. Recently, some of Katz's classical results have been generalized by Kottwitz to the context of F-crystals with additional structures and by Moonen to μ-ordinary p-divisible groups. In this paper, we discuss further generalizations to the situation of crystals in characteristic p and of p-divisible groups with additional structure by endomorphisms.

Additional Information

© Springer-Verlag 2009. Received: 2 January 2008. Accepted: 13 January 2009. Published online: 16 June 2009. We thank L. Fargues, M. Harris and R. Kottwitz for their interest in our work and for stimulating discussions. We are grateful to E. Lau, M. Rapoport and T. Wedhorn for helpful comments on a preliminary version of this paper. This project started while the authors were visiting the Institut des Hautes Études Scientifiques (E.M.) and the Université de Paris-Sud (E.V.).We thank both institutions for their hospitality. During the stay at Orsay, E.V. was supported by a fellowship within the Post-Doc program of the German Academic Exchange Service (DAAD). Later in the project, E.M. was partially supported by NSF Grant DMS-0701310.

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