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 isomorphism^{1}. 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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