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Automorphismes modérés de l'espace affine
Published online by Cambridge University Press: 20 November 2018
Résumé
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Le problème de Jung-Nagata 
$\left( cf.\,\left[ \text{J} \right],\,\left[ \text{N} \right] \right)$ consiste à savoir s'il existe des automorphismes de 
$k\left[ x,\,y,\,z \right]$ qui ne sont pas modérés. Nous proposons une approche nouvelle de cette question, fondée sur l'utilisation de la théorie des automates et du polygone de Newton. Cette approche permet notamment de généraliser de façon significative les résultats de 
$\left[ \text{A} \right]$.
Abstract
The Jung-Nagata's problem $\left( cf.\,\left[ \text{J} \right],\,\left[ \text{N} \right] \right)$ asks if there exists non-tame (or wild) automorphisms of $k\left[ x,\,y,\,z \right]$. We give a new way to attack this question, based on the automata theory and the Newton polygon. This new approch allows us to generalize significantly the results of $\left[ \text{A} \right]$.
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- Research Article
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- Copyright
- Copyright © Canadian Mathematical Society 2003
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