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- W2004701879 abstract "Nous donnons ici un contre-exemple à une vieille conjecture en théorie des singularités. Cette conjecture est que la fonction qui apparaît dans la version forte du théorème d'approximation de Artin est majorée par une fonction affine. Tout d'abord nous faisons une étude de l'approximation diophantienne entre le corps des séries en plusieurs variables et son complété pour la topologie m-adique. Nous montrons, à l'aide d'un exemple, qu'il n'existe pas de version du théorème de Liouville dans ce contexte. Ce même exemple nous fournit notre contre-exemple (théorème 1.2). Nous appliquons cela pour donner une nouvelle preuve du fait qu'il n'existe pas de théorie de l'élimination des quantificateurs pour le corps des séries en plusieurs variables. We give here a counter-example to an old conjecture in the theory of singularities. This conjecture is that the function that appears in the strong Artin approximation theorem is bounded by an affine function. First we study Diophantine approximation between the field of power series in several variables and its completion for the m-adic topology. We show, with an example, that there is no Liouville theorem in this case. This example gives us our counter-example (cf. théorème 1.2). As an application, we give a new proof of the fact that there is no theory of elimination of quantifiers for the field of fractions of the ring of power series in several variables." @default.
- W2004701879 created "2016-06-24" @default.
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- W2004701879 date "2005-11-01" @default.
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- W2004701879 title "Sur la linéarité de la fonction de Artin" @default.
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- W2004701879 doi "https://doi.org/10.1016/j.ansens.2005.10.001" @default.
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