Consider a wildly ramified
G-Galois cover of curves ϕ : Y → X branched at only one point over an algebraically
closed field k of characteristic p. In this paper, given G such that the Sylow
p-subgroups of G have order p, I show it is possible to deform ϕ to increase the
conductor at a wild ramification point. As a result, I prove that all sufficiently large
conductors occur for covers ϕ : Y → ℙk1 branched at only one point with inertia ℤ∕p.
For the proof, I show there exists such a cover with small conductor under an
additional hypothesis on G and then use deformation and formal patching to
transform this cover.
