The Stacks project

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].

Definition 26.9.1. A scheme is a locally ringed space with the property that every point has an open neighbourhood which is an affine scheme. A morphism of schemes is a morphism of locally ringed spaces. The category of schemes will be denoted $\mathit{Sch}$.

Comments (2)

Comment #917 by on

Maybe we want a historical remark here about the “prescheme/scheme” terminology, possibly with a short list of literature that is still influential but dates back to the “prescheme”-era.

Comment #921 by on

OK, I made a short historical comment on this. See here.

Post a comment

Your email address will not be published.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 toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 01IJ. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 26.9.1 as pdf