Definition 28.9.1. Let $X$ be a scheme. We say $X$ is regular, or nonsingular if for every $x \in X$ there exists an affine open neighbourhood $U \subset X$ of $x$ such that the ring $\mathcal{O}_ X(U)$ is Noetherian and regular.
Definition 28.9.1. Let $X$ be a scheme. We say $X$ is regular, or nonsingular if for every $x \in X$ there exists an affine open neighbourhood $U \subset X$ of $x$ such that the ring $\mathcal{O}_ X(U)$ is Noetherian and regular.
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