Lemma 109.16.2 (0E1N)—The Stacks project

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Part 8: Topics in Moduli Theory
Chapter 109: Moduli of Curves
Section 109.16: Smooth curves
Lemma 109.16.2 (cite)

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Lemma 109.16.2. The morphism $\mathcal{C}\! \mathit{urves}^{smooth} \to \mathop{\mathrm{Spec}}(\mathbf{Z})$ is smooth.

Proof. Follows immediately from the observation that $\mathcal{C}\! \mathit{urves}^{smooth} \subset \mathcal{C}\! \mathit{urves}^{lci+}$ and Lemma 109.15.2. $\square$

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