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.