Demazure, lectures on p-divisible groups, V.2, points of finite order and endomorphisms
Let be a field of prime characteristic .
Let be an abelian variety of dimension . Let be a prime number.
For the kernel is a finite -group of rank . We define
We have . If , then is an étale formal k-group?.
This is a free module of rank over and also a Galois module.
If , then is a -divisible group of height . In this case we define
as the Dieudonné module of . It is an F-lattice? (defined in Demazure, lectures on p-divisible groups, IV.1, isogenies) over , and in particular a free module of rank over .
For any prime , the assignation
is a functor.