The Stacks project

Definition 67.20.8. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{A}$ be a quasi-coherent sheaf of $\mathcal{O}_ X$-algebras. The relative spectrum of $\mathcal{A}$ over $X$, or simply the spectrum of $\mathcal{A}$ over $X$ is the affine morphism $\underline{\mathop{\mathrm{Spec}}}(\mathcal{A}) \to X$ corresponding to $\mathcal{A}$ under the equivalence of categories of Lemma 67.20.7.