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

Berthelot, Pierre; Messing, William

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

Citations:

Zbl 0717.00008; Zbl 0414.14014; Zbl 0516.14015