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Say I have a scheme $X$, irreducible and of finite type over a field $k$, and a closed subscheme $Y$ of $X$ with associated closed immersion $i: Y \to X$. Consider a sheaf $F$ on $X$ (for the ├ętale topology).

How should I think about the sheaf $i_* i^* F$ and the kernel of $F \to i_* i^* F$ in a more or less "concrete" way? Is it possible to visualize these sheaves somehow, or at least to compare them with $F$ in an imaginative way?

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