Demazure, lectures on p-divisible groups, II.5, the Frobenius and the Verschiebung morphism
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Let be a field with prime characteristic .
The Frobenius morphism commutes with finite products and hence if is a k-group-functor is a -group functor, too, and is a -group morphism.
We abbreviate .
The same is true for -formal groups.
Let be a commutative affine -group. Then for the Cartier dual we have
By Cartier duality we obtain the Verschiebung morphism for which holds . We abbreviate .
Let be a morphism of commutative affine -groups. The the following diagram is commutative
Moreover we have
is the identity and is zero.
This follows since is an epimorphism and and