O-displays and π-divisible formal O-modules
O-displays and π-divisible formal O-modules
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O 型显示和 π 可整除的形式 O 型模块
DOI：
10.1016/j.jalgebra.2016.03.002
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发表时间：
2016
影响因子：
0.9
通讯作者：
T. Zink
中科院分区：
文献类型：
--
作者：
Tobias Ahsendorf;Chuangxun Cheng;Chuangxun Cheng;T. Zink
本文构造了一个O-显示理论，证明了在基环上，在一定条件下，幂零O-显示范畴与π-可除形式O-模范畴是等价的.从这个结果出发，我们构造了一个Dieudonné O-显示理论，并证明了Dieudonné O-显示范畴与π-可除O-模范畴之间的类似等价性.我们还表明，这种等价性是兼容的对偶。这些结果推广了Zink和Lau关于显示和p-可除群的相应结果。
In this paper, we construct an O-display theory and prove that, under certain conditions on the base ring, the category of nilpotent O-displays and the category of π-divisible formal O-modules are equivalent. Starting with this result, we then construct a Dieudonné O-display theory and prove a similar equivalence between the category of Dieudonné O-displays and the category of π-divisible O-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.