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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