# Definition:Relative Scheme

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## 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.