ringed space

Last updated January 27, 2022

Definition

• A ringed space $(X,\mathcal{O}_X)$ is a topological space $X$ together with a sheaf $\mathcal{O}_X$ of (perhaps commutative) rings.
  • $\mathcal{O}_X$ is called the structure sheaf of $X$.
• A locally ringed space is a ringed space such that every stalk of $\mathcal{O}_X$ is a local ring.