Fermetures Integrates des Z-Algebres

Let Q denote the algebraic closure of Q in C, and Z denote its ring of integers. At the 1993 Luminy workshop on Grothendieck's theory of Dessins d'Enfants, Joseph Oesterle, wanting to know more about reduction of these Dessins modulo maximal ideals of Z, asked the following question: Let E be a finite extension of Q (T) unramified outside { 0,l,∞} ; is the normalisation of P_1√z in E finite overP_1√z? In an unpublished letter of April 17th, 1993, Y.Ihara answered this question in the affirmative, even without assuming the ramification hypothesis.