Timeline for Interpretation of elements of H^1 in sheaf cohomology.
Current License: CC BY-SA 2.5
9 events
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| Jan 29, 2010 at 22:52 | comment | added | Anweshi | @Marty. Yes, to introduce derived functors one must consider a long exact sequence of sheaves. I didn't mention this and was vague. Sorry. | |
| Jan 29, 2010 at 22:47 | comment | added | Anweshi | Is it so hard? It is there in Hartshorne, I think. | |
| Jan 29, 2010 at 22:33 | comment | added | Marty | Not really -- the "exactness breaking down" occurs when there's a short exact sequence of sheaves (not just one sheaf). Then, taking global sections of each term makes a left-exact sequence of abelian groups. This is where derived functors come into play, and a long exact sequence results. The comparison theorem between Cech cohomology and derived functor cohomology requires a bit of work -- it's a standard Grothendieck composite functor spectral sequence, I recall, with a bit of flabbiness. | |
| Jan 29, 2010 at 21:59 | comment | added | Anweshi | "sections not glueing properly" ==> Cech short exactness breaks down ==> enter derived functors ....... Anyway I have edited my post to reflect what you said. | |
| Jan 29, 2010 at 21:58 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Jan 29, 2010 at 21:44 | comment | added | Marty | This response is completely geometric, based on Cech cohomology and gluing. This response has nothing at all to do with derived functors, besides one sentence on exact sequences which is vague and not relevant to the rest of the response. | |
| Jan 29, 2010 at 21:35 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Jan 29, 2010 at 21:10 | history | edited | Anweshi | CC BY-SA 2.5 |
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| Jan 29, 2010 at 20:52 | history | answered | Anweshi | CC BY-SA 2.5 |