Reduction of covers and Hurwitz spaces

Details Reduction of covers and Hurwitz spaces Reduction of covers and Hurwitz spaces

2000-05-11

arxiv.org/abs/math/0005120v1

Mathematics

Algebraic Geometry

43 pages, 2 figures

Scientific paper

In this paper we study the reduction of Galois covers of curves, from characteristic 0 to characteristic p. The starting point is a is a recent result of Raynaud which gives a criterion for good reduction for covers of the projective line branch at 3 points. Under some condition on the Galois group, we extend this criterion to the case of 4 branch points. Moreover, we describe the reduction of the Hurwitz space of such covers and compute the number of covers with good reduction.

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