Timeline for Coherent cohomology of G/U, G = reductive group, B = TU Borel subgroup
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 14, 2011 at 20:40 | comment | added | Chuck Hague | (continued . . .) In general, that's pretty much always what one does when computing cohomology of bundles on homogeneous spaces: at some point you push down to a flag variety or partial flag variety because you can get traction there. | |
| Nov 14, 2011 at 20:40 | comment | added | Chuck Hague | This can be done in one special case: you can compute $ H^0( G/U, \mathcal O_{G/U} ) $ directly without using Borel-Weil-Bott, by using Frobenius reciprocity. My gut feeling is that this approach becomes a lot harder for computing the higher cohomology groups. If you look at Levasseur-Stafford, they ultimately push down to the flag variety and invoke Borel-Weil. (continued . . .) | |
| Nov 14, 2011 at 19:55 | comment | added | Nicolás | Thanks for the answer, Chuck. My original intention was to somehow invert the order and try to deduce the cohomology of $H^*(G/B,L)$ from the knowledge of the cohomology of $H^*(G/U,O)$. That is, I wanted to compute the latter cohomology group independently of Borel-Weil-Bott (I don't have any reason to think this should work). | |
| Nov 14, 2011 at 17:49 | history | edited | Chuck Hague | CC BY-SA 3.0 |
Yikes! Big mistake fix.
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| Nov 14, 2011 at 17:15 | history | answered | Chuck Hague | CC BY-SA 3.0 |