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Fermetures Integrates des Z-Algebres


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1 Institut De Mathematiques De Jussieu, UMR 9994, Case 247 Universite Pierre Et Marie Curie 4, Place Jussieu 75005-Paris, France
     

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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E be a finite extension of Q (T) unramified outside { 0,l,∞} ; is the normalisation of P1√z in E finite overP1√z? In an unpublished letter of April 17th, 1993, Y.Ihara answered this question in the affirmative, even without assuming the ramification hypothesis.
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  • Fermetures Integrates des Z-Algebres

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Authors

Joseph Oesterle
Institut De Mathematiques De Jussieu, UMR 9994, Case 247 Universite Pierre Et Marie Curie 4, Place Jussieu 75005-Paris, France
Layla Pharamond Dit D'costa
Institut De Mathematiques De Jussieu, UMR 9994, Case 247 Universite Pierre Et Marie Curie 4, Place Jussieu 75005-Paris, France

Abstract


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E be a finite extension of Q (T) unramified outside { 0,l,∞} ; is the normalisation of P1√z in E finite overP1√z? In an unpublished letter of April 17th, 1993, Y.Ihara answered this question in the affirmative, even without assuming the ramification hypothesis.