Example 6

Tag 0CPH, permanent. Cite it as [Bourbaki, Tag 0CPH].

Commutative Algebra, chapter VIII, § 5. Anneaux locaux réguliers

Let $X$ be an algebraic variety over a perfect field $k$ . Then $X$ is nonsingular at a point $x$ if and only if the local ring of $X$ at $x$ is regular.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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