Timeline for Comparing maps of reduced schemes
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2009 at 22:29 | comment | added | David E Speyer | I think the adjective "normal" should help a great deal here. For example, I believe that a map of finite type normal varieties, which is a bijection on points, is an isomorphism. But I don't have an answer to the original question. | |
| Nov 18, 2009 at 19:49 | answer | added | S. Carnahan♦ | timeline score: 1 | |
| Nov 5, 2009 at 10:17 | comment | added | Jose Capco | What you are asking will (in my opinion) always require a scheme theoretic condition.. For instance, your example Z⊆Y being a subscheme is already a scheme theretic condition, you require something about the rings involved in the structure sheaf. | |
| Nov 5, 2009 at 4:47 | comment | added | Andrew Critch | @Kevin: replaced K by Z. | |
| Nov 5, 2009 at 4:45 | history | edited | Andrew Critch | CC BY-SA 2.5 |
replaced K by Z
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| Nov 5, 2009 at 2:42 | comment | added | Kevin H. Lin | Ah, can you use Z or something instead of K? When I see K, I can only think "field". I suppose this is not very mathematicianly of me. It's kind of physicistly, maybe -- well, it's "field theory" after all ;-) | |
| Nov 5, 2009 at 2:01 | comment | added | S. Carnahan♦ | @KMB: Let f be the identity on the cuspidal cubic X=Y=Spec k[x,y]/(y^2-x^3), and let g be the normalization from A^1. Then there is no factorization, since k[x] doesn't map to k[x^2,x^3] in a way that commutes with the reverse inclusion. | |
| Nov 4, 2009 at 23:25 | comment | added | Kevin Buzzard | Given that no-one has bitten yet, can I explicitly ask whether people think it might hold if X and K are reduced varieties over a field? Maybe one needs X to be smooth? I'm not sure. I'm a bit concerned about the resolution of the singularity of a cuspidal cubic being a homeomorphism on the top spaces (and the map only existing in one direction in alg geo) but can't make an explicit counterexample. | |
| Nov 4, 2009 at 17:20 | history | asked | Andrew Critch | CC BY-SA 2.5 |