Lemma 70.17.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals. Let $U = \mathop{\mathrm{Spec}}(A)$ be an affine scheme étale over $X$ and let $I \subset A$ be the ideal corresponding to $\mathcal{I}|_ U$. If $X' \to X$ is the blowup of $X$ in $\mathcal{I}$, then there is a canonical isomorphism

of schemes over $U$, where the right hand side is the homogeneous spectrum of the Rees algebra of $I$ in $A$. Moreover, $U \times _ X X'$ has an affine open covering by spectra of the affine blowup algebras $A[\frac{I}{a}]$.

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