Spahn diagonalizable group scheme (Rev #2, changes)

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A diagonalizable group scheme $G$ is a group scheme satisfying the following equivalent conditions:

1. $G$ is the Cartier dual of a constant group scheme.

2. $G$ is a character group? i.e. $G$ is generated morphisms $G\to \mu_k$ into the multiplicative group.multiplicative group scheme.