Talk:Closed immersion

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About the 4th condition. Although EGA gives a proof, the following also works for me. (Forgive me if I'm missing something.)

:Assume 4. By 3 applied to $U_i$ , $U_i = \cup U_{ij} = \operatorname{Spec}(R_{ij})$ such that $f^{-1}(U_{ij}) = \operatorname{Spec}(R_{ij}/I_{ij})$ . But $U_{ij}$ are open affine in X since they are in $U_i$ . Thus, we get 3.

-- Taku (talk) 13:19, 21 August 2012 (UTC)

:I removed the fourth entry, not because I thought it to be false, but because it is not a "characterization" of closed immersions. It is a property of closed immersions and belongs in the properties section. RobHar (talk) 16:06, 21 August 2012 (UTC)

::Ok. (In case it's not obvious, I do appreciate your edits. The article looks much nicer.) -- Taku (talk) 17:28, 21 August 2012 (UTC)

Do you (or anyone else) think it makes sense to have a discussion of a separable morphism here? Glossary of scheme theory doesn't leave much room for more subtle issues. (eventually it should have its article though). -- Taku (talk) 18:03, 21 August 2012 (UTC)