Timeline for Cohomological dimension of continuous étale cohomology of finitely generated fields
Current License: CC BY-SA 4.0
15 events
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| Jul 24, 2021 at 14:36 | comment | added | Will Sawin | I think this question is probably unknown without the Tate conjecture. Suppose there did exist an $X$ with a Tate class in degree $2p$ that did not come from an algebraic cycle. Take $K$ to be the field of fractions of $X$, it is a limit over open subsets of $X$. I don't see any reason why this cohomology class should vanish after passing to an open subset. So it will give continuous cohomology in degrees $2p$ and $2p+1$ for each open subset. | |
| S Jul 4, 2021 at 4:11 | history | suggested | user308839 | CC BY-SA 4.0 |
Better title
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| Jul 4, 2021 at 4:03 | review | Suggested edits | |||
| S Jul 4, 2021 at 4:11 | |||||
| S Jul 4, 2021 at 3:58 | history | suggested | user178246 | CC BY-SA 4.0 |
Question now fully explain, and all the necessary context is given.
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| Jul 4, 2021 at 3:52 | review | Suggested edits | |||
| S Jul 4, 2021 at 3:58 | |||||
| S Jul 4, 2021 at 3:15 | history | suggested | user178246 | CC BY-SA 4.0 |
Sanity check added.
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| Jul 4, 2021 at 3:11 | review | Suggested edits | |||
| S Jul 4, 2021 at 3:15 | |||||
| S Jul 4, 2021 at 2:42 | history | suggested | user178246 | CC BY-SA 4.0 |
References provided, question clarified.
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| Jul 4, 2021 at 2:39 | review | Suggested edits | |||
| S Jul 4, 2021 at 2:42 | |||||
| Jul 3, 2021 at 22:14 | comment | added | user127776 | Yes the continuous part means considering the projective system of roots of unity as $n$ goes to infinity. | |
| Jul 3, 2021 at 22:01 | comment | added | Will Sawin | Are you meaning to take a limit as $n$ goes to $\infty$? If not, won't the group be $l^n$-torsion and then vanish after you tensor with $\mathbb Q$? | |
| Jul 3, 2021 at 21:43 | history | edited | user127776 | CC BY-SA 4.0 |
added 2 characters in body
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| Jul 3, 2021 at 21:43 | history | undeleted | user127776 | ||
| Jul 3, 2021 at 21:42 | history | deleted | user127776 | via Vote | |
| Jul 3, 2021 at 21:37 | history | asked | user127776 | CC BY-SA 4.0 |