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 $\mathit{Sch}$.

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].

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## Comments (2)

Comment #917 by Johan Commelin on

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