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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