On FF-crystalline representations

  • Bryden Cais

    Department of Mathematics Department of Mathematics University of Arizona Purdue University Tucson, Arizona 85721 West Lafayette IN 47907 USA USA
  • Tong Liu

    Department of Mathematics Department of Mathematics University of Arizona Purdue University Tucson, Arizona 85721 West Lafayette IN 47907 USA USA
On $F$-crystalline representations cover
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Abstract

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/\QF/\Q_p, and an arbitrary finite extension K/FK/F, we construct a general class of infinite and totally wildly ramified extensions K/KK_\infty/K so that the functor VVGKV\mapsto V|_{G_{K_\infty}} is fully-faithfull on the category of FF-crystalline representations VV. We also establish a new classification of FF-Barsotti-Tate groups via Kisin modules of height 1 which allows more general lifts of Frobenius.

Cite this article

Bryden Cais, Tong Liu, On FF-crystalline representations. Doc. Math. 21 (2016), pp. 223–270

DOI 10.4171/DM/532