Approximation diophantienne dans les corps de series en plusieurs variables

Details Approximation diophantienne dans les corps de series en plusieurs variables Approximation diophantienne dans les corps de series en plusieurs variables

2005-05-31

arxiv.org/abs/math/0505679v2

Mathematics

Algebraic Geometry

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

Scientific paper

We give here a result of diophantine approximation between $\O_N$, the ring of power series in several variables, and the completion of the valuation ring that dominates $\O_N$ 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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