Dans cet article nous étudions une action du groupe de Galois absolu sur des arbres planaires bicolores. A l’encontre de l’action similaire fournie par la théorie des “dessins d’enfants” de Grothendieck, l’action est induite par l’action de 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 et la comparons avec l’action de Grothendieck.
In this paper we study an action of the absolute Galois group on bicolored plane trees. In distinction with the similar action provided by the Grothendieck theory of “Dessins d’enfants” the action is induced by the action of on equivalence classes of conservative polynomials which are the simplest examples of postcritically finite rational functions. We establish some basic properties of the action 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},
pages = {205--218},
publisher = {Universit\'e Bordeaux 1},
volume = {20},
number = {1},
year = {2008},
doi = {10.5802/jtnb.622},
mrnumber = {2434164},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.622/}
}
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TI - Conservative polynomials and yet another action of $\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$ on plane trees
JO - Journal de théorie des nombres de Bordeaux
PY - 2008
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EP - 218
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IS - 1
PB - Université Bordeaux 1
UR - http://www.numdam.org/articles/10.5802/jtnb.622/
DO - 10.5802/jtnb.622
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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. http://www.numdam.org/articles/10.5802/jtnb.622/
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