OO-displays and π -divisible formal OO-modules

In this paper, we construct an OO-display theory and prove that, under certain conditions on the base ring, the category of nilpotent OO-displays and the category of π  -divisible formal OO-modules are equivalent. Starting with this result, we then construct a Dieudonné OO-display theory and prove a similar equivalence between the category of Dieudonné OO-displays and the category of π  -divisible OO-modules. We also show that this equivalence is compatible with duality. These results generalize the corresponding results of Zink and Lau on displays and p-divisible groups.