Breuil–kisin modules via crystalline cohomology

Bryden R Cais, Tong Liu

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)1199-1230
Number of pages32
JournalTransactions of the American Mathematical Society
Volume371
Issue number2
DOIs
StatePublished - Feb 1 2019

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Crystalline Cohomology
Torsion-free
P-adic
Torsional stress
Cohomology
Fiber
Crystalline materials
Ring
Module
Integer
Fibers
Narrative

Keywords

  • Breuil-Kisin modules
  • Crystalline cohomology

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Transactions of the American Mathematical Society, Vol. 371, No. 2, 01.02.2019, p. 1199-1230.

Research output: Contribution to journalArticle

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