Loading [MathJax]/extensions/tex2jax.js

The Stacks project

Lemma 71.18.5. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $Z \subset B$ be a closed subspace. Let $b : B' \to B$ be the blowing up of $Z$ in $B$. Let $g : X \to Y$ be an affine morphism of spaces over $B$. Let $\mathcal{F}$ be a quasi-coherent sheaf on $X$. Let $g' : X \times _ B B' \to Y \times _ B B'$ be the base change of $g$. Let $\mathcal{F}'$ be the strict transform of $\mathcal{F}$ relative to $b$. Then $g'_*\mathcal{F}'$ is the strict transform of $g_*\mathcal{F}$.

Proof. Omitted. Hint: Follows from the case of schemes (Divisors, Lemma 31.33.4) by étale localization (Lemma 71.18.2). $\square$


Comments (0)

There are also:

  • 2 comment(s) on Section 71.18: Strict transform

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.