## Tag `01IJ`

Chapter 25: Schemes > Section 25.9: Schemes

Definition 25.9.1. A

schemeis a locally ringed space with the property that every point has an open neighbourhood which is an affine scheme. Amorphism of schemesis a morphism of locally ringed spaces. The category of schemes will be denoted $\textit{Sch}$.

The code snippet corresponding to this tag is a part of the file `schemes.tex` and is located in lines 1601–1616 (see updates for more information).

```
\begin{definition}
\label{definition-scheme}
\begin{history}
In \cite{EGA1} what we call a scheme was called a ``pre-sch\'ema'' and the
name ``sch\'ema'' was reserved for what is a separated scheme in the
Stacks project. In the second edition \cite{EGA1-second} the terminology
was changed to the terminology that is now standard. However, one may
occasionally encounter the terminology ``prescheme'', for example in
\cite{Murre-lectures}.
\end{history}
A {\it scheme} is a locally ringed space with the property that
every point has an open neighbourhood which is an affine scheme.
A {\it morphism of schemes} is a morphism of locally
ringed spaces. The category of schemes will be denoted
$\Sch$.
\end{definition}
```

## Historical remarks

In [EGA1] what we call a scheme was called a ''pre-schéma'' and the name ''schéma'' was reserved for what is a separated scheme in the Stacks project. In the second edition [EGA1-second] the terminology was changed to the terminology that is now standard. However, one may occasionally encounter the terminology ''prescheme'', for example in [Murre-lectures].

## Comments (2)

## Add a comment on tag `01IJ`

Your email address will not be published. Required fields are marked.

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 lower-right corner).

All contributions are licensed under the GNU Free Documentation License.