Timeline for Restriction of sheaves on curves
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 28, 2014 at 14:39 | comment | added | Jason Starr | The global sections of $i^{-1}(\mathcal{F})$ are "the same as" equivalence classes of sections of $\mathcal{F}$ on open neighborhoods of $C_1$ in $C$, where two sections are equivalent if their restrictions agree on some open neighborhood of $C_1$. So your problem is roughly the same as the problem of extending a section on an open to a global section. This is always possible for flasque sheaves, but rarely possible for coherent sheaves. | |
| Jan 28, 2014 at 14:35 | comment | added | user45397 | @Starr: I am trying to understand better the concept of extending a section by zero. For instance when can I extend a section on $C_1$ to the whole of $C$. | |
| Jan 28, 2014 at 14:30 | answer | added | Jason Starr | timeline score: 1 | |
| Jan 28, 2014 at 14:23 | comment | added | Jason Starr | I am curious: where does this question come from? If you told us more about where your questions come from, perhaps MO users could provide more support than just listing counterexamples. | |
| Jan 28, 2014 at 14:00 | history | asked | user45397 | CC BY-SA 3.0 |