Lemma 70.18.9. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $\mathcal{F}$ be a finite type quasi-coherent $\mathcal{O}_ B$-module. Let $Z_ k \subset S$ be the closed subscheme cut out by $\text{Fit}_ k(\mathcal{F})$, see Section 70.5. Let $B' \to B$ be the blowup of $B$ in $Z_ k$ and let $\mathcal{F}'$ be the strict transform of $\mathcal{F}$. Then $\mathcal{F}'$ can locally be generated by $\leq k$ sections.

Proof. Omitted. Follows from the case of schemes (Divisors, Lemma 31.35.1) by étale localization (Lemma 70.18.2). $\square$

There are also:

• 2 comment(s) on Section 70.18: Strict transform

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).