The Stacks project

Definition 39.4.5. Let $S$ be a scheme. Let $(G, m)$ be a group scheme over $S$.

1. We say $G$ is a smooth group scheme if the structure morphism $G \to S$ is smooth.

2. We say $G$ is a flat group scheme if the structure morphism $G \to S$ is flat.

3. We say $G$ is a separated group scheme if the structure morphism $G \to S$ is separated.

Add more as needed.