Timeline for sheaves on products and restrictions to fibres
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 16 at 15:41 | comment | added | Hephaistos | . Thank you very much. But why is the collection of fibers on which $e$ vanishes a constructible set ? | |
| Jan 15 at 13:35 | comment | added | S. carmeli | Yes, and flatness over $S$ suffices. As if $e$ is a section which vanishes on all the infinite collection of fibers $X_s$, then since $\mathcal{E}$ is coherent, the section $e$ must vanish on the fiber at the generic point as well (the collection of fibers on which $e$ vanishes has to be a constructible set), which contradicts flatness over $S$ since it s then not torsion free as an $\mathcal{O}_S$-module. | |
| Jan 15 at 9:59 | comment | added | Hephaistos | You are right. So another hypothesis such that flatness over $S$ is needed. | |
| Jan 15 at 9:23 | history | answered | S. carmeli | CC BY-SA 4.0 |