Abhyankar's Affine Arithmetic Conjecture for the Symmetric and Alternating Groups

Alexei Entin, Noam Pirani

We prove that for any prime $p>2$, $q=p^{\nu }$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/{\mathbb{F}}_q(T)$ ramif…