Timeline for reference for (co)homology theories
Current License: CC BY-SA 3.0
6 events
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| Nov 25, 2012 at 19:37 | comment | added | Donu Arapura | Will, what I meant is that there are classes of acyclic sheaves which arise "in nature" that can be used to compute sheaf cohomology. For example, any sheaf of modules over the sheaf of $C^\infty$-functions on a manifold is acyclic, and this fact goes into the proof of the de Rham and Dolbeault theorems. | |
| Nov 25, 2012 at 18:20 | comment | added | Will Sawin | I think your use of "acyclic resolutions" is circular. Acyclic objects are objects with trivial higher cohomology. Their use in resolutions comes from repeated applications of the short exact sequence property. I think you mean to say that injective objects are acyclic. But perhaps you are using a different definition? | |
| Nov 24, 2012 at 17:34 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Nov 23, 2012 at 18:25 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Nov 23, 2012 at 16:02 | history | edited | Donu Arapura | CC BY-SA 3.0 |
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| Nov 23, 2012 at 15:57 | history | answered | Donu Arapura | CC BY-SA 3.0 |