Timeline for Criteria for coherence of rings
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2013 at 9:46 | answer | added | Fred Rohrer | timeline score: 2 | |
| Jul 25, 2013 at 18:04 | comment | added | Manny Reyes | @MartinBrandenburg, I am very late to this conversation, but I think you meant to say that it's precisely the condition that the finitely presented modules form an abelian category. | |
| Apr 30, 2011 at 18:59 | answer | added | Hagen | timeline score: 4 | |
| Jan 15, 2011 at 21:20 | answer | added | Emerton | timeline score: 8 | |
| Jan 15, 2011 at 20:58 | comment | added | Donu Arapura | Yes, right. I think the idea of coherence of sheaves goes back to the work of Cartan and Oka in several complex variables. | |
| Jan 15, 2011 at 20:52 | answer | added | user12235 | timeline score: 5 | |
| Jan 15, 2011 at 20:40 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
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| Jan 15, 2011 at 17:03 | comment | added | Mariano Suárez-Álvarez | My guess is that the idea must have preexisted FAC in the analytic case. Cartan, maybe? (Although that's pretty much like saying «in Euler»...!) | |
| Jan 15, 2011 at 13:50 | comment | added | Donu Arapura | Also, see Serre "Faisceaux Algebriques Coherent", Annals 1955, page 210 for a definition of coherence for a sheaf of commutative rings. | |
| Jan 15, 2011 at 9:14 | comment | added | Kevin Buzzard | +1 Martin! Coherence is introduced very early on in EGA in this context (so presumably Grothendieck knew about the notion in the early 60s). Somehow one reason it's less widely-known is, I guess, that when Hartshorne wrote his book he stuck to the Noetherian case for simplicity, so just defined a coherent sheaf of modules as one which locally looked like a f.g. module, so one doesn't see the subtlety of the definition in the non-Noeth case. Course this is all in the commutative case, but EGA is a place to look [look in index for "coherent"...] | |
| Jan 15, 2011 at 8:45 | comment | added | Martin Brandenburg | 1+. I don't think that coherence is just a technical condition. It's the best condition for that the category of finitely generated modules is abelian. Due to laziness, we often restrict to noetherian rings for this. | |
| Jan 15, 2011 at 6:02 | history | asked | Mariano Suárez-Álvarez | CC BY-SA 2.5 |