Sheaf Associated to Injective Module over Noetherian Ring is Flasque

Theorem

Let $A$ be a Noetherian commutative ring.

Let $I$ be an injective $A$-module.

Then the sheaf $\tilde I$ associated to $I$ on $\Spec A$ is flasque.

Proof

This theorem requires a proof. In particular: Hartshorne III.3.4 You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1977: Robin Hartshorne: Algebraic Geometry Proposition $\text{III}.3.4$