The Stacks project

Definition 28.10.1. Let $X$ be a scheme.

1. The dimension of $X$ is just the dimension of $X$ as a topological spaces, see Topology, Definition 5.10.1.

2. For $x \in X$ we denote $\dim _ x(X)$ the dimension of the underlying topological space of $X$ at $x$ as in Topology, Definition 5.10.1. We say $\dim _ x(X)$ is the dimension of $X$ at $x$.