Timeline for relative cohomology $H(X,D)$ of a pair in Weil cohomology theory
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 30, 2014 at 15:10 | comment | added | S. Carnahan♦ | If $D$ is a (well-behaved) divisor, you can take the log de Rham complex as a proxy for relative cochains. | |
| May 30, 2014 at 5:19 | comment | added | Qiaochu Yuan | Relative cohomology is the cohomology of the mapping cone, so what one needs is an algebro-geometric mapping cone. At the level of schemes there doesn't seem to be a reasonable way to do this due to the lack of a reasonable substitute for the interval. Etale cohomology only depends on the etale (pro)homotopy type, so you ought to be able to take the mapping cone in (pro)homotopy types in that case. In general I guess you want something like a model structure on simplicial schemes to be able to talk about mapping cones in the latter. | |
| May 29, 2014 at 18:29 | history | asked | mmm | CC BY-SA 3.0 |