Abstract

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.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 737-768
Launched on MUSE
2002-08-01
Open Access
No
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.