Timeline for Integral model of etale covering
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 2, 2019 at 5:48 | comment | added | Todd Trimble | @cardinal math.stackexchange.com/questions/1633326/… | |
| May 31, 2019 at 20:38 | comment | added | user74900 | what is a hyperbolic curve? | |
| May 15, 2018 at 8:21 | comment | added | Ariyan Javanpeykar | Did you mean to write prime-to-$p$ degree? The answer would then be positive; look up "tame fundamental group" for instance. However, if you really meant $p$-power degree, then the answer is negative, because of the Artin-Schreier covers. | |
| May 15, 2018 at 0:26 | comment | added | User0829 | @AriyanJavanpeykar Thank you. If I restrict myself to finite etale coverings of $\overline{\mathcal{X}}_k$ of $p$-power degree, do I still have negative answer? - the reason for asking this question is, in a paper published in a renowned journal, I found a similar claim stated without any proof (the author said that it is almost trivial fact for experts). | |
| May 14, 2018 at 18:52 | comment | added | Ariyan Javanpeykar | You are right. I misread that. My apologies. The answer to your question is still negative though. Choose $X\to \mathbb{A}^1$ finite etale with $X$ hyperbolic. If I recall correctly such covers exist. Now pull-back Artin-Schreier covers to $X$. | |
| May 13, 2018 at 2:39 | comment | added | User0829 | @AriyanJavanpeykar Why is $\mathbb{P}^1_K$ hyperbolic under my definition? I said a "curve" is a smooth geometrically connected scheme of dimension 1, NOT "hyperbolic curve". | |
| May 12, 2018 at 17:42 | comment | added | Ariyan Javanpeykar | With your definition, $\mathbb{P}^1_K$ is a hyperbolic curve. That's probably not what you want. In any case, you are asking whether finite etale covers of a curve over $\overline{\mathbb{F}_p}$ lift. With your definitions, a simple counterexample of non-liftable covers are the Artin-Schreier covers of the affine line. | |
| May 11, 2018 at 12:24 | history | asked | User0829 | CC BY-SA 4.0 |