English

Approximation diophantienne dans les corps de series en plusieurs variables

Algebraic Geometry 2007-05-23 v2 Complex Variables

Abstract

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

Keywords

Cite

@article{arxiv.math/0505679,
  title  = {Approximation diophantienne dans les corps de series en plusieurs variables},
  author = {Guillaume Rond},
  journal= {arXiv preprint arXiv:math/0505679},
  year   = {2007}
}

Comments

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

R2 v1 2026-07-22T17:20:07.536Z