Exercise 111.39.1. Let R be a ring. Let R \to k be a map from R to a field. Let n \geq 0. Show that
\mathop{\mathrm{Mor}}\nolimits _{\mathop{\mathrm{Spec}}(R)}(\mathop{\mathrm{Spec}}(k), \mathbf{P}^ n_ R) = (k^{n + 1} \setminus \{ 0\} )/k^*
where k^* acts via scalar multiplication on k^{n + 1}. From now on we denote (x_0 : \ldots : x_ n) the morphism \mathop{\mathrm{Spec}}(k) \to \mathbf{P}^ n_ k corresponding to the equivalence class of the element (x_0, \ldots , x_ n) \in k^{n + 1} \setminus \{ 0\} .
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