Timeline for Global sections of higher direct image sheaf
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Mar 1, 2016 at 17:11 | vote | accept | Ron | ||
| Feb 29, 2016 at 22:48 | answer | added | Sándor Kovács | timeline score: 4 | |
| Feb 28, 2016 at 18:05 | comment | added | Ray Hoobler | But that is not enough to answer the question since $H^0(X-S,R^1 j_*\mathcal{O}_{X-S}) = Ker[H^0(X-S,R^2j_*\mathcal{O}_{X-S}) \rightarrow H^2(X,\mathcal{O}_X)]$. | |
| Feb 28, 2016 at 7:46 | comment | added | abx | $R^1j_*\mathcal{O}_{X\smallsetminus S}$ is a sheaf supported on $S$, with fiber at $s\in S$ the group $H^2_{\{s\} }(\mathcal{O}_X)$, which is nonzero. See SGA2, §I and II. | |
| Feb 28, 2016 at 7:33 | history | edited | Ron | CC BY-SA 3.0 |
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| Feb 28, 2016 at 6:11 | history | edited | Ron | CC BY-SA 3.0 |
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| Feb 28, 2016 at 5:37 | comment | added | Ron | @abx I am a bit confused. I know this fact. I do not understand, whether this proves or disproves the question. Could you please elaborate a bit more? | |
| Feb 28, 2016 at 3:56 | comment | added | abx | $j_*\mathcal{O}_{X\smallsetminus S}$ is isomorphic to $\mathcal{O}_X$. | |
| Feb 28, 2016 at 2:29 | comment | added | Ron | @dhy I have edited the question. | |
| Feb 28, 2016 at 2:29 | history | edited | Ron | CC BY-SA 3.0 |
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| Feb 28, 2016 at 2:13 | comment | added | dhy | Is there any reason to believe something like this should be true? I don't see why there should be any natural map between the two and it's false for $S$ empty... | |
| Feb 28, 2016 at 1:41 | history | asked | Ron | CC BY-SA 3.0 |