Timeline for Criterion for an etale cover $E[\ell]\to \mathbb{G}_m$ to be tamely ramified in $0, \infty$
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Jan 3 at 23:18 | review | Close votes | |||
| Jan 18 at 3:08 | |||||
| Jan 3 at 22:57 | comment | added | R. van Dobben de Bruyn | The action of $\pi_1(\mathbf G_m)$ on a geometric fibre $E_{\bar x}[\ell]$ for $\bar x \colon \operatorname{Spec} \overline{\kappa(x)} \to \mathbf G_m$ is by linear automorphisms, so lands in $\operatorname{GL}_2(\mathbf Z/\ell\mathbf Z)$ (instead of merely the symmetric group on $\ell^2$ elements). Tamely ramified means that the action of the inertia subgroups at $0$, $1$, and $\infty$ factors through a quotient whose order is prime to $p$, but the whole group has order prime to $p$. | |
| Jan 3 at 21:42 | history | asked | user267839 | CC BY-SA 4.0 |