On The Inertia Conjecture for Alternating group Covers

Abstract

The wild part of Abhyankar's Inertia Conjecture for a product of certain Alternating groups is shown for any algebraically closed field of odd characteristic. For $d$ a multiple of the characteristic of the base field, a new \'etale $A_d$-cover of the affine line is obtained using an explicit equation and it is shown that it has the minimal possible upper jump.