Talk:Closed immersion

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)