Breuil–kisin modules via crystalline cohomology

Bryden Cais, Tong Liu

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish (US)
Pages (from-to)1199-1230
Number of pages32
JournalTransactions of the American Mathematical Society
Issue number2
StatePublished - Feb 1 2019


  • Breuil-Kisin modules
  • Crystalline cohomology

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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