Timeline for Can injective modules over R give non-injective sheaves over Spec R?
Current License: CC BY-SA 2.5
8 events
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| Feb 10, 2010 at 14:45 | comment | added | Mariano Suárez-Álvarez | @Emerton: A counterexample to the non-noetherian case, I guess? | |
| Feb 9, 2010 at 20:29 | comment | added | Emerton | Adam Topaz's answer to the question linked to by VA gives a counterexample (although I didn't check the reference). | |
| Feb 9, 2010 at 6:21 | comment | added | Mariano Suárez-Álvarez | Added the chapter, which is always nice to have. | |
| Feb 9, 2010 at 6:20 | history | edited | Mariano Suárez-Álvarez | CC BY-SA 2.5 |
added 14 characters in body
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| Feb 9, 2010 at 6:04 | comment | added | Anton Geraschenko | Just to clarify, it's Corollary 7.14 of Chapter II. This is a pretty surprising result to me. It means that the counterexample Allen was asking for probably requires you to think of an example of an injective module I over a non-noetherian ring R, a non-quasi-coherent ("incoherent"?) sheaf F on Spec(R), and a non-split injection I→F. Injective modules, non-noetherian rings, and incoherent sheaves are pretty hard for me to think about individually; putting them all together may be hopeless. | |
| Feb 9, 2010 at 5:15 | comment | added | VA. | See also this answer: mathoverflow.net/questions/6762/… | |
| Feb 9, 2010 at 5:15 | comment | added | Mariano Suárez-Álvarez | Of course, there exists non-noetherian rings... Hic sunt dracones. | |
| Feb 9, 2010 at 5:10 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 2.5 |