Timeline for My first question - on Affine Schemes in Algebraic Geometry
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2015 at 20:37 | comment | added | Ingo Blechschmidt | @ChristopherTownsend, that claim of Peter is discussed on the nForum, with no clear consensus. One thing to note is that the "pullback square" in question only commutes up to a non-invertible natural transformation. | |
| Apr 12, 2013 at 16:26 | answer | added | Sean Tilson | timeline score: 3 | |
| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
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| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
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| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
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| S Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
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| Feb 28, 2012 at 9:01 | vote | accept | Christopher Townsend | ||
| S Feb 28, 2012 at 9:01 | |||||
| Feb 28, 2012 at 9:01 | comment | added | Christopher Townsend | @Peter Arndt, I thought through what you said. Viewing rings as geoemtric morphisms, I can't see how every affine scheme can be a pullback of toposes as described. The morphism being pulled back is a subtopos morphism from one classifying topos(that of local rings) to another (that of rings). It's pullback will be a subtopos of Set, and these correspond [I think] to sublocales of 1 and not to coherent locales in general, which they must for the caracterization to work. I am sure you are right, but perhaps you can see my difficult in agreeing the characterisation? | |
| Feb 24, 2012 at 1:10 | answer | added | Anton Fetisov | timeline score: 0 | |
| Feb 23, 2012 at 21:51 | comment | added | Peter Arndt | An affine scheme is a ringed topos arising as a pullback of topoi, namely as the pullback of a morphism from the topos of sets to the classifying topos of rings along the forgetful morphism from the classifying topos of local rings to the topos of rings - see this answer for more details: mathoverflow.net/questions/8204/… | |
| Feb 23, 2012 at 14:26 | answer | added | Martin Brandenburg | timeline score: 10 | |
| Feb 23, 2012 at 12:56 | comment | added | Zhen Lin | In terms of pure point set topology, there is a complete characterisation of spectral spaces. | |
| Feb 23, 2012 at 9:54 | answer | added | Mark Grant | timeline score: 10 | |
| Feb 23, 2012 at 9:29 | answer | added | Sasha | timeline score: 19 | |
| Feb 23, 2012 at 9:07 | history | asked | Christopher Townsend | CC BY-SA 3.0 |