Dieudonne theory over semiperfect rings and perfectoid rings

Lau E. Dieudonne theory over semiperfect rings and perfectoid rings. Compositio Mathematica. 2018;154(9):1974-2004.The Dieudonne crystal of a p-divisible group over a semiperfect ring R can be endowed with a window structure. If R satisfies a boundedness condition, this construction gives an equivalence of categories. As an application we obtain a classification of p-divisible groups and commutative finite locally free p-group schemes over perfectoid rings by Breuil Kisin Fargues modules if p >= 3