Windows for Displays of p-Divisible Groups

Abstract

The starting point of this work was the classification ofp-divisible groups over a discrete valuation ring of characteristic 0 with perfect residue field of characteristicp> 3 obtained by C. Breuil in his note [[B]. We will show that such a classification holds under quite general circumstances. We prove this by showing that the category used by Breuil to classifyp-divisible groups is equivalent to the category of Dieudonne displays, which we defined in[Z-DD]. Breuil obtains his result by a very useful classification of finite fiat group schemes over a discrete valuation ring as above. We have no generalization of such a classification.