Definition 27.4.5. Let $S$ be a scheme. Let $\mathcal{A}$ be a quasi-coherent sheaf of $\mathcal{O}_ S$-algebras. The *relative spectrum of $\mathcal{A}$ over $S$*, or simply the *spectrum of $\mathcal{A}$ over $S$* is the scheme constructed in Lemma 27.3.4 which represents the functor $F$ (27.4.0.1), see Lemma 27.4.4. We denote it $\pi : \underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A}) \to S$. The “universal family” is a morphism of $\mathcal{O}_ S$-algebras

\[ \mathcal{A} \longrightarrow \pi _*\mathcal{O}_{\underline{\mathop{\mathrm{Spec}}}_ S(\mathcal{A})} \]

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