Timeline for Is $H_{et}^1(X,F) = H^1(\pi_1^{et}(X), F(\bar{k}))$ true?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 14, 2017 at 0:02 | vote | accept | user108289 | ||
| Apr 13, 2017 at 3:36 | comment | added | Keerthi Madapusi | There is a natural morphism $\pi$ of sites from the etale site of $X$ to its finite etale site. Using the Leray spectral sequence, your question basically reduces to asking: Is $R^1\pi_*F = 0$? Since $R^1\pi_*F$ is the sheafication of $U\mapsto H^1_{et}(U,F)$ over the finite etale site, another way of saying this is: If $U$ is a $k$-scheme, then does every $F$-torsor admit a section over a finite etale $U$-scheme? The answer is yes, simply because $F$ is itself finite etale over $k$ (since we are in characteristic $0$). | |
| Apr 13, 2017 at 1:01 | answer | added | Marc Hoyois | timeline score: 10 | |
| Apr 12, 2017 at 7:59 | review | First posts | |||
| Apr 12, 2017 at 8:04 | |||||
| Apr 12, 2017 at 7:58 | history | asked | user108289 | CC BY-SA 3.0 |