Timeline for What is the étale fundamental group of projective spaces over finite fields?
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6 events
| when toggle format | what | by | license | comment | |
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| Feb 17, 2021 at 22:48 | comment | added | Ben Wieland | The fundamental group does not respect products. That requires either completeness or coprime characteristic, so it's ok here, but it's not true in general. If it were true, then the fundamental group of a group scheme would be abelian. But it's not for $\mathbb A^1$. @Faris | |
| Feb 17, 2021 at 18:03 | comment | added | R. van Dobben de Bruyn | See for example Tag 0BTX combined with the computation of $\pi_1(\mathbf P^n_{\bar k})$. (See here for a fun Riemann–Hurwitz-free proof when $n=1$.) | |
| Feb 17, 2021 at 14:09 | comment | added | Faris | The fundamental group of $\mathbb{P}^n_{\overline{\mathbb{F}_q}}$ can be computed by noting that the fundamental group $\mathbb{P}^1_{\overline{\mathbb{F}_q}}$ is trivial, that the fundamental group of a direct product is the direct product of the fundamental groups and that fundamental group is a birational invariant. | |
| Feb 17, 2021 at 10:57 | review | Close votes | |||
| Feb 18, 2021 at 21:25 | |||||
| Feb 17, 2021 at 10:38 | comment | added | abx | This is just the Galois group $\operatorname{Gal}(\overline{\mathbb{F}_q}/\mathbb{F}_q) $. | |
| Feb 17, 2021 at 9:56 | history | asked | hennlu | CC BY-SA 4.0 |