Lemma 38.37.2. Consider an almost blow up square (38.37.0.1). Let $W \to X'$ be a closed immersion of finite presentation. The following are equivalent

$X' \setminus E$ is scheme theoretically contained in $W$,

the blowup $X''$ of $X$ in $Z$ is scheme theoretically contained in $W$,

the diagram

\[ \xymatrix{ E \cap W \ar[d] \ar[r] & W \ar[d] \\ Z \ar[r] & X } \]is an almost blow up square. Here $E \cap W$ is the scheme theoretic intersection.

## Comments (0)