Definition 64.12.1. Let $S \in \mathop{\mathrm{Ob}}\nolimits (\mathit{Sch}_{fppf})$ be a scheme. Let $F$ be an algebraic space over $S$.

1. A morphism of algebraic spaces over $S$ is called an open immersion if it is representable, and an open immersion in the sense of Definition 64.5.1.

2. An open subspace of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is an open immersion.

3. A morphism of algebraic spaces over $S$ is called a closed immersion if it is representable, and a closed immersion in the sense of Definition 64.5.1.

4. A closed subspace of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is a closed immersion.

5. A morphism of algebraic spaces over $S$ is called an immersion if it is representable, and an immersion in the sense of Definition 64.5.1.

6. A locally closed subspace of $F$ is a subfunctor $F' \subset F$ such that $F'$ is an algebraic space and $F' \to F$ is an immersion.

There are also:

• 4 comment(s) on Section 64.12: Immersions and Zariski coverings of algebraic spaces

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).