Lemma 71.18.6. Let S be a scheme. Let B be an algebraic space over S. Let Z \subset B be a closed subspace. Let D \subset B be an effective Cartier divisor. Let Z' \subset B be the closed subspace cut out by the product of the ideal sheaves of Z and D. Let B' \to B be the blowup of B in Z.
The blowup of B in Z' is isomorphic to B' \to B.
Let f : X \to B be a morphism of algebraic spaces and let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. If the subsheaf of \mathcal{F} of sections supported on |f^{-1}D| is zero, then the strict transform of \mathcal{F} relative to the blowing up in Z agrees with the strict transform of \mathcal{F} relative to the blowing up of B in Z'.
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