Definition:Relative Scheme

Definition

Let $S$ be a scheme.

A (relative) scheme over $S$ is a morphism of schemes $p : X \to S$ for some scheme $X$.

Also denoted as

The way relative schemes are described varies. The following formulations are all equivalent:

• $X \to S$ is a (relative) scheme (over $S$).
• $p$ is a (relative) scheme (over $S$).
• $X$ is a (relative) scheme (over $S$).
• $X/S$ is a (relative) scheme (over $S$).

In every sentence above at most one of the brackets can be dropped.