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If $f:X\longrightarrow Y$ is a proper lisse morphism and $\mathcal{F}$ is a torsion sheaf on $X$ then one has: $$ (R^{i}f_{*}\mathcal{F})_{\overline{y}}\cong H_{c}^{i}(X_{\overline{y}},\mathcal{F}_{|X_{\overline{y}}}) $$ For any geometric point $\overline{y}$ of $Y$. I am wondering if this result can be extended to other kind of sheaf, e.g. if $\mathcal{F}=\mathbb{Q}_{l}$ or $\mathcal{F}$ is constructible. Thank you in advance

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