### Abstract

For a perfect field k of characteristic p > 0 and a smooth and proper formal scheme X over the ring of integers of a finite and totally ramified extension K of W (k)[1/p], we propose a cohomological construction of the Breuil–Kisin module attached to the p-adic étale cohomology H
_{ét}
^{i}
(X
_{K}
, Z
_{p}
). We then prove that our proposal works when p > 2, i < p − 1, and the crystalline cohomology of the special fiber of X is torsion-free in degrees i and i + 1.

Original language | English (US) |
---|---|

Pages (from-to) | 1199-1230 |

Number of pages | 32 |

Journal | Transactions of the American Mathematical Society |

Volume | 371 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2019 |

### Fingerprint

### Keywords

- Breuil-Kisin modules
- Crystalline cohomology

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*371*(2), 1199-1230. https://doi.org/10.1090/tran/7280

**Breuil–kisin modules via crystalline cohomology.** / Cais, Bryden R; Liu, Tong.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 371, no. 2, pp. 1199-1230. https://doi.org/10.1090/tran/7280

}

TY - JOUR

T1 - Breuil–kisin modules via crystalline cohomology

AU - Cais, Bryden R

AU - Liu, Tong

PY - 2019/2/1

Y1 - 2019/2/1

N2 - For a perfect field k of characteristic p > 0 and a smooth and proper formal scheme X over the ring of integers of a finite and totally ramified extension K of W (k)[1/p], we propose a cohomological construction of the Breuil–Kisin module attached to the p-adic étale cohomology H ét i (X K , Z p ). We then prove that our proposal works when p > 2, i < p − 1, and the crystalline cohomology of the special fiber of X is torsion-free in degrees i and i + 1.

AB - For a perfect field k of characteristic p > 0 and a smooth and proper formal scheme X over the ring of integers of a finite and totally ramified extension K of W (k)[1/p], we propose a cohomological construction of the Breuil–Kisin module attached to the p-adic étale cohomology H ét i (X K , Z p ). We then prove that our proposal works when p > 2, i < p − 1, and the crystalline cohomology of the special fiber of X is torsion-free in degrees i and i + 1.

KW - Breuil-Kisin modules

KW - Crystalline cohomology

UR - http://www.scopus.com/inward/record.url?scp=85062195828&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062195828&partnerID=8YFLogxK

U2 - 10.1090/tran/7280

DO - 10.1090/tran/7280

M3 - Article

AN - SCOPUS:85062195828

VL - 371

SP - 1199

EP - 1230

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -