Approximation diophantienne dans les corps de series en plusieurs variables

2005/05/31 by Guillaume Rond, Rond, Guillaume
Mathematics · #11J25 #14B05 #32S99 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:11J25 #msc:14B05 #msc:32S99

paper · pdf · doi:10.48550/arxiv.math/0505679

to appear in Annales de l'Institut Fourier, few changes following referee's comments

arxiv created 2005/09/23 · arxiv updated 2009/12/01

Abstract

We give here a result of diophantine approximation between Ø_N, the ring of power series in several variables, and the completion of the valuation ring that dominates Ø_N for the \m-adic topology. We deduce from this that the Artin function of a homogenous polynomial in two variables is bounded by an affine function, which can be interpreted in term of a Lojasiewicz inequality on the wedges space.

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