Crystalline representations and F-crystals

Abstract

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.