If $f : Y \to X$ is a morphism of schemes and $Z \subset X$ is a locally closed subscheme, then there is a natural pullback map $f^* : H_ Z(\mathcal{F}) \to H_{f^{-1}Z}(f^{-1}\mathcal{F})$.
If $f : Y \to X$ is a morphism of schemes and $Z \subset X$ is a locally closed subscheme, then there is a natural pullback map $f^* : H_ Z(\mathcal{F}) \to H_{f^{-1}Z}(f^{-1}\mathcal{F})$.
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