Timeline for An example computation of etale cohomology
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Apr 23, 2016 at 13:01 | history | edited | Turbo |
edited tags
|
|
| Mar 25, 2010 at 17:47 | comment | added | Ben Webster♦ | David- My personal feeling is that if you said it on MO (or any public forum), and haven't deleted it, then it's fair game to quote. | |
| Mar 25, 2010 at 16:02 | comment | added | David Hansen | @Moonface: Ahhh, let me guess - by a Leray spectral sequence, computing H^2(X) is reduced to computing H^1(C,H^1(fiber)), and since H^1(fiber) is a local system of $\mathbb{F}_5^{4}$'s you trivialize it by passing to a $5^4$-fold cover. | |
| Mar 25, 2010 at 15:58 | comment | added | David Hansen | @Ben: I wasn't sure about the etiquette for quoting other people's answers to previous questions, hence the elliptical wording. I have edited it for clarity. | |
| Mar 25, 2010 at 15:58 | history | edited | David Hansen | CC BY-SA 2.5 |
added 90 characters in body; added 24 characters in body
|
| Mar 25, 2010 at 15:50 | comment | added | moonface | Correction to previous comment: The cover $C' \rightarrow C$ defined by $5$-torsion in relative Jacobian isn't Galois; indeed, we are only interested in a "certain piece" of its cohomology, but I'm not sure how to find this "piece" without passing to the "Galois closure"... And the Galois closure of $C' \rightarrow C$ is a cover of monstrous degree indeed. | |
| Mar 25, 2010 at 15:42 | comment | added | Ben Webster♦ | David- The way you wrote this question is extremely confusing. I think it would have been really helpful to include part of moonface's comment as an actual quote. | |
| Mar 25, 2010 at 15:40 | comment | added | moonface | In that question, we were working with mod $5$ coefficients. Also, $125$ should have been $625$. Finally, it is not "equivalent": you need only a piece of the cohomology of the cover. Specifically, if $f : X \rightarrow C$, let $C'$ be the $5$-torsion in the relative Jacobian; its Galois group is a subgroup of $\mathrm{GSp}(\mathbb{F}_5)$, and you need roughly the piece of the cohomology of $C'$ through which $G$ acts by the standard representation. | |
| Mar 25, 2010 at 15:18 | history | asked | David Hansen | CC BY-SA 2.5 |