Abstract

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 suficiently large conductors occur for covers φ : Y → P_k¹ 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.

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