Timeline for Varieties with only top $\ell$-adic cohomology not vanish?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2016 at 14:56 | comment | added | Will Sawin | @user148212 Yes, and even further I think people are suggesting that you may have to throw away a larger finite set of primes. | |
| Feb 26, 2016 at 13:04 | comment | added | user148212 | Thanks a lot. It seems in the counter-example there will be some problem on char=2 (as 2 appears in the denominator of the construction of the group action) ? | |
| Feb 26, 2016 at 12:52 | comment | added | David E Speyer | The hard part is showing that the characteristic p fibers don't become isomorphic to affine space. I think that will require actually reading the references. | |
| Feb 25, 2016 at 22:59 | comment | added | Donu Arapura | David, yes, I think it's doable also. After spreading the variety out over a finitely generated ring, you can use the comparison theorem + proper base change. | |
| Feb 25, 2016 at 21:36 | comment | added | David E Speyer | I think the counterexamples in the answer to mathoverflow.net/questions/7603/… should also be counterexamples for your question. (Leaving this as a comment and not an answer because I didn't think through the details of switching between $\mathbb{C}$ and $\overline{\mathbb{F}_p}$ for large $p$, but it should be doable.) | |
| Feb 25, 2016 at 21:26 | history | edited | user148212 |
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| Feb 24, 2016 at 13:15 | history | asked | user148212 | CC BY-SA 3.0 |