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.

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