The Stacks project

Definition 29.20.1. Let $X$ be a scheme.

  1. We say $X$ is quasi-excellent if for every $x \in X$ there exists an affine open neighbourhood $x \in U \subset X$ such that the ring $\mathcal{O}_ X(U)$ is quasi-excellent (see More on Algebra, Definition 15.53.1).

  2. We say $X$ is excellent if for every $x \in X$ there exists an affine open neighbourhood $x \in U \subset X$ such that the ring $\mathcal{O}_ X(U)$ is excellent (see More on Algebra, Definition 15.53.1).

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View Definition 29.20.1 as pdf