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The Stacks project

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}).
[1] Often one imposes the assumption that \mathcal{A} is generated by \mathcal{A}_1 over \mathcal{O}_ S. We do not assume this in order to be consistent with [II, (8.3.1), EGA].

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