The Stacks project

Lemma 99.15.10. The stack in groupoids $\mathcal{X} = \mathcal{C}\! \mathit{urves}$ satisfies openness of versality over $\mathop{\mathrm{Spec}}(\mathbf{Z})$. Similarly, after base change (Remark 99.15.5) openness of versality holds over any Noetherian base scheme $S$.

Proof. This is immediate from the fully faithful embedding (99.15.1.1) and the corresponding fact for $\mathcal{S}\! \mathit{paces}'_{fp, flat, proper}$ (Lemma 99.13.9). $\square$

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