Hi.

If $f\rightarrow S$ is an open morphism with fibers of dimension n of reduced finite dimensionnal complex spaces (or universally open morphism with fibers of dimension n of locally noetherian, excellents and without embedded components or reduced schemes) it is true that

$f^{*}G$ torsion free for all torsion free coherent sheaf $G$ on $S$ $\Longrightarrow$ $f$ is flat ?

Thank you.

Hi.

Let $f\rightarrow S$ be an open morphism of reduced finite dimensional complex spaces (or a universally open morphism of locally noetherian excellents without embedded components or reduced schemes) with fibers of dimension $n$.

If $f^{*}G$ is torsion free for all torsion free coherent sheaves $G$ on $S$, then is it true that $f$ is flat ?

Thank you.