Timeline for Is there a "Hilbert syzygy theorem" for smooth manifolds? Or: does every finitely generated $C^\infty$ module have a finite-length resolution in vector bundles?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Oct 7, 2010 at 5:31 | comment | added | Torsten Ekedahl | There is a stronger condition, the existence of a (possibly infinite) resolution of f.g. projectives. I doubt that even that would be sufficient however. | |
| Oct 7, 2010 at 4:06 | comment | added | Tom Goodwillie | Finite presentation does not suffice, it seems. | |
| Oct 7, 2010 at 1:14 | vote | accept | Theo Johnson-Freyd | ||
| Oct 7, 2010 at 1:02 | comment | added | Daniel Pomerleano | Since your ring is non-Noetherian, you might have to build in a coherency condition or at least require that the module be of finite presentation. Or you could allow for projective modules of infinite rank. If your interests are cohomological, it is true that on a smooth compact manifold sheaf cohomology of, I think, any sheaf of abelian groups vanishes above the dimension n. The reference is "Sheaves on Manifolds". | |
| Oct 7, 2010 at 0:20 | answer | added | Tom Goodwillie | timeline score: 13 | |
| Oct 6, 2010 at 23:44 | history | asked | Theo Johnson-Freyd | CC BY-SA 2.5 |