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Approximation diophantienne dans les corps de series en plusieurs variables

Guillaume Rond
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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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Guillaume Rond. 2005-09-23. Approximation diophantienne dans les corps de series en plusieurs variables. https://arxiv.org/abs/math/0505679

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