### Abstract

Let k be a perfect field of characteristic p > 2 and K an extension of F = FracW(k) contained in some F(μ_{pr} ). Using crystalline Dieudonné; theory, we provide a classification of p-divisible groups over R = O_{K}[[t_{1},. ., t_{d}]] in terms of finite height (Ρ, τ)-modules over S := W(k)[[u, t_{1},. ., t_{d}]]. When d = 0, such a classification is a consequence of (a special case of) the theory of Kisin-Ren; in this setting, our construction gives an independent proof of this result, and moreover allows us to recover the Dieudonné; crystal of a p-divisible group from the Wach module associated to its Tate module by Berger-Breuil or by Kisin-Ren.

Original language | English (US) |
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Pages (from-to) | 733-763 |

Number of pages | 31 |

Journal | Proceedings of the London Mathematical Society |

Volume | 114 |

Issue number | 4 |

DOIs | |

State | Published - 2017 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Cais, B. R., & Lau, E. (2017). Dieudonné; crystals and Wach modules for p-divisible groups.

*Proceedings of the London Mathematical Society*,*114*(4), 733-763. https://doi.org/10.1112/plms.12021