Timeline for Finiteness of De Rham cohomology of smooth quasi-projective varieties
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2014 at 16:08 | vote | accept | Hugo Chapdelaine | ||
| Jan 28, 2014 at 21:55 | answer | added | Misha Verbitsky | timeline score: 7 | |
| Jan 26, 2014 at 21:20 | comment | added | Hugo Chapdelaine | Ok nice. So then it is enough to show that on a smooth affine variety, the De Rham cohomology is finite dimensional. Do we always have the existence of a FINITE open good cover (in the topological sense) on smooth affine varieties? | |
| Jan 26, 2014 at 20:58 | comment | added | abx | For the Zariski topology, yes. | |
| Jan 26, 2014 at 20:56 | comment | added | Hugo Chapdelaine | Does quasi-projective imply quasi-compact in the Zariski topology? Anyhow, it is not clear to me that you can find a finite open good cover for $U$... | |
| Jan 26, 2014 at 18:01 | comment | added | abx | $H_{dR}^*(U^{\infty},\mathbf{R})$ looks like the usual $C^\infty$ de Rham cohomology, which is finite dimensional by the standard de Rham theorem. What you mean is probably the algebraic de Rham cohomology $H_{dR}^*(U,\mathbf{C})$. | |
| Jan 26, 2014 at 15:15 | answer | added | David E Speyer | timeline score: 3 | |
| Jan 26, 2014 at 14:39 | answer | added | Jason Starr | timeline score: 4 | |
| Jan 26, 2014 at 14:32 | history | asked | Hugo Chapdelaine | CC BY-SA 3.0 |