Conservative polynomials and yet another action of Gal( ¯/) on plane trees
Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 1, p. 205-218
Dans cet article nous étudions une action D du groupe de Galois absolu Γ=Gal( ¯/) 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 l’action 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 l’action de Grothendieck.
In this paper we study an action D of the absolute Galois group Γ=Gal( ¯/) 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 postcritically finite rational functions. We establish some basic properties of the action D and compare it with the Grothendieck action.
@article{JTNB_2008__20_1_205_0,
     author = {Pakovich, Fedor},
     title = {Conservative polynomials and yet another action of $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on plane trees},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {20},
     number = {1},
     year = {2008},
     pages = {205-218},
     doi = {10.5802/jtnb.622},
     mrnumber = {2434164},
     zbl = {pre05543197},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2008__20_1_205_0}
}
Pakovich, Fedor. Conservative polynomials and yet another action of $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on plane trees. Journal de théorie des nombres de Bordeaux, Tome 20 (2008) no. 1, pp. 205-218. doi : 10.5802/jtnb.622. https://www.numdam.org/item/JTNB_2008__20_1_205_0/

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