Timeline for Generalization of the Leray-Hirsch theorem
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 11, 2021 at 0:31 | comment | added | Dan Petersen | If it's a trivial local system on a dense open it's really easy to compute the intermediate extension! | |
| Apr 11, 2021 at 0:28 | comment | added | user43198 | @DanPetersen Yes, by "... is the same" I mean the same Betti numbers. Also, on an open dense subset of X it is going to be a local system (using the theorem on generic smoothness). Why does same Betti numbers imply local system? And could you elaborate a bit more on what application of the decomposition theorem you have in mind. | |
| Apr 11, 2021 at 0:24 | comment | added | Dan Petersen | I interpreted "...is the same" as saying that all fibers have the same Betti numbers. It's not clear to me what assumption to add to deduce that the higher direct images are trivial local systems. One observation is that by the decomposition theorem it would be enough to prove it on a dense open subset of X. | |
| Apr 10, 2021 at 23:35 | comment | added | user43198 | Could you give a reference or idea on how to prove that $R^qf_*\mathbb{Q}$ is a local system? | |
| Apr 10, 2021 at 23:29 | history | answered | Donu Arapura | CC BY-SA 4.0 |