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Journal Article

Conservative polynomials and yet another action of Gal (ℚ̄/ℚ) on plane trees

Fedor PAKOVICH
Journal de Théorie des Nombres de Bordeaux
Vol. 20, No. 1 (2008), pp. 205-218
Stable URL: http://www.jstor.org/stable/43972932
Page Count: 14
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Conservative polynomials and yet another action of Gal (ℚ̄/ℚ) on plane trees
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Abstract

Dans cet article nous étudions une action D du groupe de Galois absolu Γ = Gal (ℚ/ℚ) sur des arbres planaires bicolores. A l'encontre de l'action similaire fournie par la théorie des "dessins d'enfants" de Grothendieck, l'action D est induite par Faction de Γ sur des classes d'équivalence de polynômes conservateurs qui sont les exemples les plus simples de fonctions rationnelles finies postcritiques. Nous établissons les propriétés principales de l'action D et la comparons avec Faction de Grothendieck. In this paper we study an action D of the absolute Galois group Γ = Gal (ℚ/ℚ) on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of "Dessins d'enfants" the action D is induced by the action of Γ on equivalence classes of conservative polynomials which are the simplest examples of post critically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.

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