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By a similar discussion (replacing $p$ by $F$) as in § 8, we have:
If $G$ is is a connected finite type formal group, define
This is a module over the $F$-completion $\hat D_k$ of $D_k$.
The Dieudonné-functor is an equivalence
between the category of connected formal groups of finite type and the category of $\hat D_k$-modules $M$ such that $M/FM$ has finite length. Moreover we have:
$G$ is finite iff $M(G)$ has finite length iff $F^n M(G)=0$ for large $n$.
$G$ is smooth iff $F:M(G)\to M(G)$ is injective. In that case $dim(G)= length(M(G)/ FM(G))$.