The Stacks project

Lemma 110.47.1. There exists an affine scheme $X = \mathop{\mathrm{Spec}}(A)$ and an injective $A$-module $J$ such that $\widetilde{J}$ is not a flasque sheaf on $X$. Even the restriction $\Gamma (X, \widetilde{J}) \to \Gamma (U, \widetilde{J})$ with $U$ a standard open need not be surjective.

Proof. See above. $\square$

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