
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 the terminology was changed to the terminology that is now standard. However, one may occasionally encounter the terminology “prescheme”, for example in .

Definition 25.9.1. 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 $\mathit{Sch}$.

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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