In this paper, I investigate wildly ramified G-Galois covers of curves [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] branched at exactly one point over an algebraically closed field k of characteristic p. I answer a question of M. Raynaud by showing that proper families of such covers of a twisted projective line are isotrivial. The method is to construct an affine moduli space for covers whose inertia group is of the form [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]. There are two other applications of this space in the case that [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /]. The first uses formal patching to compute the dimension of the space of nonisotrivial deformations of φ in terms of the lower jump of the filtration of higher inertia groups. The second gives necessary criteria for good reduction of families of such covers. These results will be used in a future paper to prove the existence of such covers φ with specified ramification data.


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pp. 737-768
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