Definition 105.4.3. We say a morphism $S \to \mathcal{M}_{1, 1}$ is *smooth* if for every morphism $S' \to \mathcal{M}_{1, 1}$ the projection morphism

\[ S \times _{\mathcal{M}_{1, 1}} S' \longrightarrow S' \]

is smooth.

Definition 105.4.3. We say a morphism $S \to \mathcal{M}_{1, 1}$ is *smooth* if for every morphism $S' \to \mathcal{M}_{1, 1}$ the projection morphism

\[ S \times _{\mathcal{M}_{1, 1}} S' \longrightarrow S' \]

is smooth.

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