Lemma 53.2.8 (0BY3)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 53: Algebraic Curves
Section 53.2: Curves and function fields
Lemma 53.2.8 (cite)

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Lemma 53.2.8. Let $k$ be a field. Let $X$ be a curve and let $Y$ be the nonsingular projective model of $X$ . If $k$ is perfect, then $Y$ is a smooth projective curve.

Proof. See Varieties, Lemma 33.43.8 for example. $\square$

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