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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