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Charles Siegel
Charles Siegel
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Hi.

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

Thanks.

Hi.

I want to know if for $f:X--->S$ 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), $G-->H^{-n}(f^{!}G)$ and $G-->f^{*}G\otimes w_{X/S}$ agree...

Thanks.

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.

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kaddar
kaddar
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Relative canonical sheaf

Hi.

I want to know if for $f:X--->S$ 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), $G-->H^{-n}(f^{!}G)$ and $G-->f^{*}G\otimes w_{X/S}$ agree...

Thanks.