Proposition 31.17.9. Let $\pi : X \to Y$ be a finite surjective morphism of schemes. Assume that $X$ has an ample invertible $\mathcal{O}_ X$-module. If

$\pi $ is finite locally free, or

$Y$ is an integral normal scheme, or

$Y$ is Noetherian, $p\mathcal{O}_ Y = 0$, and $X = Y_{red}$,

then $Y$ has an ample invertible $\mathcal{O}_ Y$-module.

## Comments (2)

Comment #3764 by Zhiyu Zhang on

Comment #3895 by Johan on