Definition 27.7.1. Let S be a scheme. Let \mathcal{A} be a quasi-coherent graded \mathcal{O}_ S-algebra. Assume that \mathcal{O}_ S \to \mathcal{A}_0 is an isomorphism1. The cone associated to \mathcal{A} or the affine cone associated to \mathcal{A} is
C(\mathcal{A}) = \underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A}).
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