On f-crystalline representations

Bryden R Cais, Tong Liu

Research output: Contribution to journalArticle

3 Citations (Scopus)

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/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
Volume21
Issue number2016
StatePublished - 2016

Fingerprint

Frobenius
Module
Functor
Arbitrary
Coefficient
Class

Keywords

  • F-crystalline representations
  • Kisin modules

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

On f-crystalline representations. / Cais, Bryden R; Liu, Tong.

In: Documenta Mathematica, Vol. 21, No. 2016, 2016, p. 223-270.

Research output: Contribution to journalArticle

Cais, BR & Liu, T 2016, 'On f-crystalline representations', Documenta Mathematica, vol. 21, no. 2016, pp. 223-270.
Cais, Bryden R ; Liu, Tong. / On f-crystalline representations. In: Documenta Mathematica. 2016 ; Vol. 21, No. 2016. pp. 223-270.
@article{16118e9dfa4c4a9ebbfaf460e7a478cf,
title = "On f-crystalline representations",
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/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.",
keywords = "F-crystalline representations, Kisin modules",
author = "Cais, {Bryden R} and Tong Liu",
year = "2016",
language = "English (US)",
volume = "21",
pages = "223--270",
journal = "Documenta Mathematica",
issn = "1431-0635",
publisher = "Deutsche Mathematiker Vereinigung",
number = "2016",

}

TY - JOUR

T1 - On f-crystalline representations

AU - Cais, Bryden R

AU - Liu, Tong

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - F-crystalline representations

KW - Kisin modules

UR - http://www.scopus.com/inward/record.url?scp=85006025177&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006025177&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:85006025177

VL - 21

SP - 223

EP - 270

JO - Documenta Mathematica

JF - Documenta Mathematica

SN - 1431-0635

IS - 2016

ER -