Reduction of covers and Hurwitz spaces

Irene I. Bouw; Stefan Wewers

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arXiv · math/0005120

Reduction of covers and Hurwitz spaces

Irene I. Bouw·Stefan Wewers

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Abstract

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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Irene I. Bouw, Stefan Wewers. 2000-05-11. Reduction of covers and Hurwitz spaces. https://arxiv.org/abs/math/0005120

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