On f-crystalline representations

Bryden R Cais, Tong Liu

Research output: Contribution to journalArticle

3 Scopus citations


We extend the theory of Kisin modules and crystalline representations to allow more general coefficient fields and lifts of Frobenius. In particular, for a finite and totally ramified extension F/Qp, and an arbitrary finite extension K/F, we construct a general class of infinite and totally wildly ramified extensions K/K so that the functor V 7 V =(pipe)GK∞ is fully-faithfull on the category of Fcrystalline representations V. We also establish a new classification of F-Barsotti-Tate groups via Kisin modules of height 1 which allows more general lifts of Frobenius.

Original languageEnglish (US)
Pages (from-to)223-270
Number of pages48
JournalDocumenta Mathematica
Issue number2016
StatePublished - 2016


  • F-crystalline representations
  • Kisin modules

ASJC Scopus subject areas

  • Mathematics(all)

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    Cais, B. R., & Liu, T. (2016). On f-crystalline representations. Documenta Mathematica, 21(2016), 223-270.