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Apr 13, 2021 at 7:14 comment added Stabilo Outch! Thank you two very much, for both comments.
Apr 12, 2021 at 14:14 comment added Bugs Bunny And you do know that there is no left adjoint already in the affine case: math.stackexchange.com/questions/3055802/…
Apr 12, 2021 at 14:12 comment added abx This is not true. Take $X=\operatorname{Spec}(A) $, with $A$ a Gorenstein ring of Krull dimension $0$; then $\mathscr{O}_X$ is injective. Now take $Z= \operatorname{Spec}(B) $, where $B$ is a quotient of $A$ which is not Gorenstein; then $\mathscr{O}_Z=i^*\mathscr{O}_X$ is not injective.
Apr 12, 2021 at 13:58 history edited Francesco Polizzi CC BY-SA 4.0
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Apr 12, 2021 at 13:47 history edited Stabilo CC BY-SA 4.0
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Apr 12, 2021 at 12:52 history asked Stabilo CC BY-SA 4.0