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.