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Mathematische Zeitschrift

, Volume 287, Issue 3–4, pp 1255–1277 | Cite as

The almost product structure of Newton strata in the Deformation space of a Barsotti–Tate group with crystalline Tate tensors

  • Paul Hamacher
Article

Abstract

In this paper, we construct the almost product structure of the minimal Newton stratum in deformation spaces of Barsotti–Tate groups with crystalline Tate tensors, similar to Oort’s and Mantovan’s construction for Shimura varieties of PEL-type. It allows us to describe the geometry of the Newton stratum in terms of the geometry of two simpler objects, the central leaf and the isogeny leaf. This yields the dimension and the closure relations of the Newton strata in the deformation space. In particular, their nonemptiness shows that a generalisation of Grothendieck’s conjecture of deformations of Barsotti–Tate groups with given Newton polygon holds. As an application, we determine analogous geometric properties of the Newton stratification of Shimura varieties of Hodge type and prove the equidimensionality of Rapoport–Zink spaces of Hodge type.

Notes

Acknowledgements

I am grateful to Mark Kisin for many helpful discussions and his advice. I warmly thank Thomas Lovering for giving me a preliminary version of his thesis. I thank Stephan Neupert and Eva Viehmann for pointing out some mistakes in the preliminary version of this article.

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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Technische Universität MünchenGarching bei MünchenGermany

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