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4 votes
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Is the restriction of an injective sheaf on a closed subscheme still injective?

Let $X$ be a Noetherian scheme, and let $i:Z\to X$ be the inclusion of a closed subscheme $Z$. Let $\mathcal{I}$ be an injective sheaf of modules on $X$. Question. Is $i^*\mathcal{I}$ still an ...
1 vote
2 answers
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Pullback of a constant sheaf

Let $\varphi:X\to Y$ be a surjective morphism of schemes which are connected and of finite type. Let $A$ be an abelian group, $\mathscr{F}$ be the constant sheaf on $X$ with fibers $A$ and $\mathscr{...