Is the following statement true? if so where can I find a proof for reference purposes?
- Direct limit of injective étale sheaves of abelian groups on a Noetherian scheme is injective.
This goes back whether the extension property of being injective can be checked over finitely presented sheaves or not. I was not able to figure that out.
Upon writing this question it was suggested to me to checkout the Hartshorne's chapter III problem 2.6. Which is not about étale sheaves but rather sheaves on Noetherian topological spaces. Furthermore the exercise seems to be incorrect (at least the hint is incorrect not sure about the statement of the exercise itself). You can read this post to realize why it is incorrect.