Timeline for answer to Etale cohomology and l-adic Tate modules by Jared Weinstein
Current License: CC BY-SA 2.5
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11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 11, 2009 at 2:07 | vote | accept | Jonah Sinick | ||
| Dec 11, 2009 at 2:07 | history | bounty awarded | Jonah Sinick | ||
| Dec 10, 2009 at 6:07 | comment | added | Jonah Sinick | Jared - Thanks for your further response. At first blush I can't tell whether or not the procedure that you suggest has a priori bounded running time, but it's interesting to see the appearance of point counting (mod p) again. As you might expect, I was looking for a more canonical/direct construction of K from V, but I have gotten the sense from responses that if such a thing exists, it is likely unknown and not immediate from the definition of etale cohomology. I will think more about your remarks...thanks also to moonface. | |
| Dec 10, 2009 at 5:35 | comment | added | moonface | Nope. I have no idea about it at all. I don't even have interesting examples of projective smooth varieties with such torsion. Maybe it's a good topic for a question here... | |
| Dec 10, 2009 at 4:00 | comment | added | Jared Weinstein | That's a really good point, moonface. Do you have a fix for this? How would you detect torsion in the 5-adic cohomology? | |
| Dec 10, 2009 at 3:27 | comment | added | moonface | There's a distinction between the mod 5 etale cohomoology and the reduction of the $\mathbb{Q}_5$ cohomology. What you discuss above would in principle detect (the semisimplification of the) latter, not the former; they will differ if there is torsion in the $\mathbb{Z}_5$-cohomology. (I also missed this in my comment below.) | |
| Dec 10, 2009 at 3:15 | history | edited | Jared Weinstein | CC BY-SA 2.5 |
added 1978 characters in body; edited body
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| Dec 1, 2009 at 16:16 | comment | added | Jared Weinstein | Minhyong: You're absolutely right. Can you give a short explanation of the relationship? | |
| Dec 1, 2009 at 9:11 | comment | added | Minhyong Kim | I'm sorry to make only an unconstructive remark, but I thought I should point out that your first isomorphism is not exactly a tautology. | |
| Dec 1, 2009 at 5:14 | comment | added | Jonah Sinick | Jared - Thanks. What you describe is very pretty and has taught me something new. I don't yet see the Galois action on the etale side, but I will think about this. | |
| Dec 1, 2009 at 3:37 | history | answered | Jared Weinstein | CC BY-SA 2.5 |