Definition:Relative Scheme
Jump to navigation
Jump to search
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.
This article, or a section of it, needs explaining. In particular: "brackets can be dropped" -- what does that mean? You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by explaining it. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Explain}} from the code. |
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |