This entry is about a section of the text
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 $dim(G)= length(M(G)/ FM(G))$.
Last revised on May 27, 2012 at 13:49:18. See the history of this page for a list of all contributions to it.