2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59179In 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.43 pages, 2 figuresAlgebraic Geometry14H30;14G32text