Timeline for étale covers and torsion line bundles
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 9, 2013 at 15:51 | answer | added | Francesco Polizzi | timeline score: 7 | |
| Jul 9, 2013 at 8:48 | review | First posts | |||
| Jul 9, 2013 at 8:59 | |||||
| Jul 9, 2013 at 8:48 | comment | added | user36795 | Hi Jason, thanks for the counterexample! I'm actually interested in the situation when the base field contains the roots of unity of order $|G|$. How do you prove the statement in that case? | |
| Jul 9, 2013 at 8:47 | history | edited | user36795 | CC BY-SA 3.0 |
added 72 characters in body
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| Jul 9, 2013 at 8:41 | comment | added | Jason Starr | That is not true without further hypotheses. For instance, let $X$ be $\mathbb{P}^1_{\mathbb{R}}$. Let $G=\mathbb{Z}/2\mathbb{Z}$ act via the involution $[x,y]\mapsto [y,-x]$. Then the quotient $Y$ does not have any invertible sheaf $L$ of degree $-1$, a necessary condition for your assertion to hold. You either need to assume that your field contains appropriate roots of unity, or you should replace $G$ by a group scheme whose Cartier dual is split, e.g., $G=\mathbf{\mu}_n$. | |
| Jul 9, 2013 at 8:28 | history | asked | user36795 | CC BY-SA 3.0 |