## 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) |
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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 |

## Keywords

- Breuil-Kisin modules
- Crystalline cohomology

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics