Crystalline representations and F-crystals

  • Mark Kisin
Part of the Progress in Mathematics book series (PM, volume 253)


Following ideas of Berger and Breuil, we give a new classification of crystalline representations. The objects involved may be viewed as local, characteristic 0 analogues of the “shtukas” introduced by Drinfeld. We apply our results to give a classification of p-divisible groups and finite flat group schemes, conjectured by Breuil, and to show that a crystalline representation with Hodge-Tate weights 0, 1 arises from a p-divisible group, a result conjectured by Fontaine.


Group Scheme Full Subcategory Divided Power Coherent Sheaf Unique Lift 
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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • Mark Kisin
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA

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