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Théorie de Dieudonné cristalline. III: Théorèmes d’équivalence et de pleine fidélité. (Dieudonné crystalline theory. III: Theorems of equivalence and of full faith). (French) Zbl 0753.14041
The Grothendieck Festschrift, Collect. Artic. in Honor of the 60th Birthday of A. Grothendieck. Vol. I, Prog. Math. 86, 173-247 (1990).
[For the entire collection see Zbl 0717.00008; for part I see Astérisque 63, 17-38 (1979; Zbl 0414.14014); part II appeared as book, Lect. Notes Math. 930 (1982; Zbl 0516.14015).]
This is the third in the series of papers devoted to Dieudonné crystalline theory. In the paper under review the authors prove some results announced in part I (loc. cit.). The authors study faithfulness properties of the Dieudonné crystalline functor.
As an application, the authors show that on a liftable proper smooth simply-connected variety each $$p$$-divisible group is isoconstant, i.e. isogenous to a constant $$p$$-divisible group.
Reviewer: F.L.Zak (Moskva)

##### MSC:
 14L05 Formal groups, $$p$$-divisible groups
##### Keywords:
Dieudonné crystalline theory; $$p$$-divisible group
##### Biographic References:
Grothendieck, Alexander