Hartshorne mention at the beginning of section 4 in chapter 2 that the definition of separated is similliar to hausdorff. We all can see that. That is also what I found in google. Again - we all can see that so i dont find it helpfull enough. I guess that one can truly understand the "true nature" of the definition after working enough with schemes, but I still have a feeling that maybe I am missing something since separation appears, for example, when defining curves, etc.. Why is it so important for us? What will we get, for example, if we drop the separation axiom? Where the separation takes its part when defining curves for "actually being curves" as we would like them to behave?
2026-03-30 03:36:20.1774841780
Motivation for separated and proper schemes
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