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The Stacks project

Definition 71.11.3. Let S be a scheme. Let X be an algebraic space over S. Let \mathcal{A} be a quasi-coherent sheaf of graded \mathcal{O}_ X-algebras. The relative homogeneous spectrum of \mathcal{A} over X, or the homogeneous spectrum of \mathcal{A} over X, or the relative Proj of \mathcal{A} over X is the algebraic space F over X of Lemma 71.11.2. We denote it \pi : \underline{\text{Proj}}_ X(\mathcal{A}) \to X.


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