Timeline for A more general form of Grauert's Theorem on Higher Direct Image Sheaves?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2013 at 19:25 | answer | added | Ravi Vakil | timeline score: 4 | |
| Jan 13, 2013 at 6:06 | comment | added | anon | @Piotr: What you suggest fails for $X = A \times A^t$, $Y = A^t$, $f$ the natural projection, and $F$ being the Poincare line bundle for an abelian variety $A$ of dimension $g$. Indeed, $R^i f_*(F) = 0$ for $i < g$, but the same is not true for the fibre over $0$. | |
| Jan 9, 2013 at 21:35 | answer | added | Angelo | timeline score: 5 | |
| Dec 12, 2012 at 20:28 | answer | added | jlk | timeline score: 2 | |
| Dec 12, 2012 at 0:50 | comment | added | Piotr Achinger | You can still hope that the following holds: suppose $f:X\to Y$ and $\mathcal{F}$ are like in your first sentence. Then if $R^i f_*(\mathcal{F})$ is locally free on $Y$, then $R^i f_*(\mathcal{F})$ commutes with base change. This I think is true and follows from the discussion of cohomology and base change in Mumford's "Abelian varieties". | |
| Dec 11, 2012 at 21:09 | comment | added | Damian Rössler | See mathoverflow.net/questions/114238/… | |
| Dec 11, 2012 at 15:12 | history | asked | HNuer | CC BY-SA 3.0 |