### 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) |
---|---|

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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Proceedings of the London Mathematical Society*,

*114*(4), 733-763. https://doi.org/10.1112/plms.12021

**Dieudonné; crystals and Wach modules for p-divisible groups.** / Cais, Bryden R; Lau, Eike.

Research output: Contribution to journal › Article

*Proceedings of the London Mathematical Society*, vol. 114, no. 4, pp. 733-763. https://doi.org/10.1112/plms.12021

}

TY - JOUR

T1 - Dieudonné; crystals and Wach modules for p-divisible groups

AU - Cais, Bryden R

AU - Lau, Eike

PY - 2017

Y1 - 2017

N2 - Let k be a perfect field of characteristic p > 2 and K an extension of F = FracW(k) contained in some F(μpr ). Using crystalline Dieudonné; theory, we provide a classification of p-divisible groups over R = OK[[t1,. ., td]] in terms of finite height (Ρ, τ)-modules over S := W(k)[[u, t1,. ., td]]. 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.

AB - Let k be a perfect field of characteristic p > 2 and K an extension of F = FracW(k) contained in some F(μpr ). Using crystalline Dieudonné; theory, we provide a classification of p-divisible groups over R = OK[[t1,. ., td]] in terms of finite height (Ρ, τ)-modules over S := W(k)[[u, t1,. ., td]]. 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.

UR - http://www.scopus.com/inward/record.url?scp=85025131021&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85025131021&partnerID=8YFLogxK

U2 - 10.1112/plms.12021

DO - 10.1112/plms.12021

M3 - Article

AN - SCOPUS:85025131021

VL - 114

SP - 733

EP - 763

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

SN - 0024-6115

IS - 4

ER -