Definition 27.13.2. The scheme \mathbf{P}^ n_{\mathbf{Z}} = \text{Proj}(\mathbf{Z}[T_0, \ldots , T_ n]) is called projective n-space over \mathbf{Z}. Its base change \mathbf{P}^ n_ S to a scheme S is called projective n-space over S. If R is a ring the base change to \mathop{\mathrm{Spec}}(R) is denoted \mathbf{P}^ n_ R and called projective n-space over R.
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