Lemma 53.19.14. Let $k'/k$ be a finite separable field extension. Let $X$ be a locally algebraic $k'$-scheme of dimension $1$. Let $x \in X$ be a closed point. The following are equivalent

1. $x$ is a node, and

2. $x$ is a node when $X$ viewed as a locally algebraic $k$-scheme.

Proof. Follows immediately from the characterization of nodes in Lemma 53.19.7. $\square$

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