Timeline for DeRham cohomology
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2011 at 16:59 | comment | added | Donu Arapura | Take a look at mathoverflow.net/questions/17937/… for further discussion. | |
| Apr 1, 2011 at 7:25 | comment | added | chemaida | Ok..thank you for your responses..I would be interested in the subtle reason that Donu alludes to or even a reference | |
| Mar 31, 2011 at 16:00 | comment | added | Donu Arapura | chemaida, to be clear, the Poincar\'e lemma holds for holomorphic or $C^\infty$ forms, but it can fail for the algebraic de Rham complex even in characteristic $0$ (which is what Piotr was referring to). Nevertheless the hypercohomology of the algebraic de Rham complex does give the correct answer, although the reasons are more subtle. | |
| Mar 31, 2011 at 15:16 | comment | added | chemaida | in char o the deRham is a resolution of C , which implies $H(X,C) \cong H_{Dr}(X)$ | |
| Mar 31, 2011 at 13:05 | comment | added | Piotr Achinger | It fails even in char.0, because the Poincare lemma works only formally locally and the de Rham complex is not exact in positive degrees. On the other hand, the cohomology of any constant sheaf vanishes on an irreducible topological space, so anyway taking resolutions of $k$ would not lead no anything of interest. | |
| Mar 31, 2011 at 8:27 | comment | added | Leo Alonso | Have you heard about crystalline cohomology? (see en.wikipedia.org/wiki/Crystalline_cohomology) It is not really a resolution of the local system $k$, though... | |
| Mar 31, 2011 at 7:44 | history | asked | chemaida | CC BY-SA 2.5 |