Definition 39.4.5. Let $S$ be a scheme. Let $(G, m)$ be a group scheme over $S$.
We say $G$ is a smooth group scheme if the structure morphism $G \to S$ is smooth.
We say $G$ is a flat group scheme if the structure morphism $G \to S$ is flat.
We say $G$ is a separated group scheme if the structure morphism $G \to S$ is separated.
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