Timeline for Smooth in codimension-k and the weight filtration
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2011 at 23:05 | answer | added | AFK | timeline score: 1 | |
| May 11, 2011 at 19:28 | answer | added | Remke Kloosterman | timeline score: 4 | |
| May 11, 2011 at 11:01 | answer | added | Donu Arapura | timeline score: 4 | |
| May 11, 2011 at 0:57 | answer | added | SGP | timeline score: 1 | |
| May 11, 2011 at 0:11 | comment | added | shenghao | uh... maybe one uses de Jong's alteration to reduce to the proper smooth case, and for that we may apply the proper smooth base change to reduce to $k=\overline{\mathbb F}_p.$ Not sure if it's too difficult to check the abutment filtr. is indep. of the choice of the alteration though... | |
| May 10, 2011 at 23:46 | comment | added | shenghao | Sorry, but I'm afraid I didn't see what you are hoping for, e.g. what is the "fact" you mentioned? Do you have a conjectural nontrivial bound for the weight? BTW, if char. $k=0$ one can reduce to $\mathbb C$ and use Hodge theory to get the weight filtration, but if char. $k=p,$ I don't really see how to reduce to $k=\overline{F}_p$ to get the wt. filtr. (unless you start with finite fields): somewhere when doing spreading out, we cannot compare the cohom. of the special fiber with that of the generic fiber, as $X$ is not smooth. Or maybe I'm wrong...? | |
| May 10, 2011 at 23:32 | comment | added | David E Speyer | Unfortunately, I want to use such a fact inside a proof by contradiction, so the concrete situation is one that I am trying to show is impossible and thus can't look at examples of. I can tell you that I am looking at projective varieties (but that should affect the other end of the weight filtration) and that they are normal (so automatically smooth in codimension 1) if that helps. | |
| May 10, 2011 at 23:20 | comment | added | shenghao | Maybe you already tried this: the long exact sequence induced by decomposing $X$ into the smooth part and the rest. This seems not of too much help in the general situation, or at least one needs, I guess, to do some dévissage, as the sequence involves $H^k_Z(X)$ and purity doesn't apply directly. But if you have some concrete situation in mind, this might be of a little help. | |
| May 10, 2011 at 23:01 | history | asked | David E Speyer | CC BY-SA 3.0 |