Lemma 71.17.2. 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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