Timeline for Commutativity between functors on sheaves of abelian groups
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2018 at 23:11 | comment | added | BrianT | Thank you very much for your answer, it helps me a lot. When you say « sufficiently nice spaces », can you tell me what you mean ? Finally, about 5) from what you are saying, the functor $i_* i^!$ gives relative cohomology. However, it is defined for a closed subset A. Do we have a similar definition for A open ? Does this functor commute with direct sums ? | |
| Aug 27, 2018 at 20:51 | comment | added | Yonatan Harpaz | I edited the answer to provide a bit more information. I don't have a reference for (3) but you should be able to find information by searching "cohomology with support", and maybe also "exceptional inverse image". | |
| Aug 27, 2018 at 20:47 | history | edited | Yonatan Harpaz | CC BY-SA 4.0 |
added 1364 characters in body
|
| Aug 27, 2018 at 15:02 | comment | added | BrianT | Thanks @Yonatan. 1) do you have an idea of when it could hold, for instance, if $f : X := Y \times F \to Y$ is the natural projection, and $A$ doesn't project to a point ? 3) how could we obtain a sheaf on $X$ with the functor $i^!$ ? Don't we need to use the direct image too ? Do you know a reference in which I can find a definition of relative cohomology in terms of these functors ? 4) provided that we have such a definition of relative cohomology, when could we have this commutativity property ? 5) my question is, when does the functor "relative cohomology" commute with direct sums ? | |
| Aug 27, 2018 at 13:52 | history | answered | Yonatan Harpaz | CC BY-SA 4.0 |