Hi.

I want to know if for $f:X\to S$ a proper flat holomorphic map with n-dimensionnal fibers over reduced complex space S, the relative canonical sheaf $w_{X/S}:=H^{-n}(f^{!}O_{S})$ is a dualizing sheaf which imply that the two functor, on Coh(S), $G\to H^{-n}(f^{!}G)$ and $G \to f^{*}G\otimes w_{X/S}$ agree...

Thanks.