Lemma 107.20.4. The morphisms $\mathcal{C}\! \mathit{urves}^{prestable} \to \mathop{\mathrm{Spec}}(\mathbf{Z})$ and $\mathcal{C}\! \mathit{urves}^{prestable}_ g \to \mathop{\mathrm{Spec}}(\mathbf{Z})$ are smooth.

**Proof.**
Since $\mathcal{C}\! \mathit{urves}^{prestable}$ is an open substack of $\mathcal{C}\! \mathit{urves}^{nodal}$ this follows from Lemma 107.18.2.
$\square$

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