Timeline for Can the Category of Schemes be Concretized?
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Mar 18, 2014 at 20:15 | history | edited | Tim Campion | CC BY-SA 3.0 |
Updated in response to Zhen Lin's answer.
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| Mar 18, 2014 at 19:23 | history | edited | Tim Campion | CC BY-SA 3.0 |
Updated answer based on results of another MO question.
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| Mar 11, 2014 at 11:41 | comment | added | Zhen Lin | A scheme is much more than just a ring. It's not even obvious to me whether the underlying continuous map of a regular monomorphism has to be injective, let alone be a topological embedding; and on the ring side, it's not obvious that the morphism of structure sheaves has to be an epimorphism, let alone a regular one. | |
| Mar 11, 2014 at 11:14 | comment | added | Tim Campion | Well, in the category of rings, epimorphisms are subtle, but regular epis are surjective, so rather less pathological. In particular, affine schemes are regularly well-powered, though of course we already knew from David Speyer's answer that affine schemes are concretizable... Are there additional sources of subtlety that affect even the regular monos of schemes? | |
| Mar 11, 2014 at 8:21 | comment | added | Zhen Lin | Finitely complete – yes. But monomorphisms are quite subtle and I would not dare to speculate on wellpoweredness... | |
| Mar 11, 2014 at 2:40 | history | answered | Tim Campion | CC BY-SA 3.0 |