Abhyankar's affine arithmetic conjecture for the symmetric and alternating groups

We prove that for any prime p > 2, q = p(nu) a power of p, n >= p and G = S-n or G = A(n) (symmetric or alternating group), there exists a Galois extension K/F-q(T) ramified only over infinity with Gal(K/F-q(T)) = G. This confirms a conjecture of Abhyankar for the case of symmetric and alternating groups over finite fields of odd characteristic.(c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper proves the existence of a Galois extension with ramification only at infinity for symmetric and alternating groups over finite fields of odd characteristic.