I have seen statements like this " Fermat curve is a wild Galois cover of $\mathbb{P}_{k}^{1}$ ramified at $\{0,1, \infty\}$." Here, $k$ is a field of characteristic $p>0$. I would like to understand what it precisely means.
Here by Fermat curve $F_n$ we mean $\operatorname{Proj}(k[x,y,x]/(x^n+y^n-z^n)$. Now, the usual map from $\phi:F_n \to \mathbb{P}_{k}^{1}$ which is flat and unramified at all points except at $\{0,1, \infty\}$. Now since this cover is Galois, I expect $Aut(F_n,\mathbb{P}_{k}^{1}) = \operatorname{deg}(\phi)$.
Is the above interpretation correct? Also, what is the group $Aut(F_n,\mathbb{P}_{k}^{1})$ here?