= Sheafification of an injective module is flasque
{title2=$I\text{ injective over }A\implies\widetilde I\text{ flasque}$}
For a <Noetherian ring> $A$, an <injective module> $I$ gives a <flasque sheaf> on $\operatorname{Spec}A$. If $U=\operatorname{Spec}A\setminus V(\mathfrak a)$, clearing denominators on finitely many principal opens identifies $\Gamma(U,\widetilde I)$ with $\varinjlim_n\operatorname{Hom}_A(\mathfrak a^n,I)$. Each map extends to $A$ by injectivity. Thus every section on $U$ extends globally, and all restriction maps are surjective. This concerns sheafification of an injective module, rather than the different assertion that an <injective sheaf of modules> is flasque.
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