## Beware of the Two Galois Actions

Let $F$ be a field and $E/F$ be a nontrivial Galois extensions with Galois group $\Gamma$. If $V$ is an $F$-scheme then the points $V(E)$ carry a natural action of $\Gamma$ via the action on $\mathrm{Spec}(E)$. Sometimes, however, $V$ might have two Galois actions. How does this arise? Perhaps the most natural setting is when […]