Abstract: This talk discusses joint work with Rachel Pries. We study the following question. Given G, for which I and h does there exist a G-Galois cover of the affine line in characteristic p with inertia group I and conductor h. The answer is closely related to the `arithmetic' of covers in characteristic zero. For G equal to A_p or PSL_2(p), we show that all possible inertia groups occur, but that the set of conductors that occur depends on the group.