About the algebraic closure of the field of power series in several variables in characteristic zero Auteur(s): Rond G. (Document sans référence bibliographique) 2015-03-27 Ref HAL: hal-01313076_v1 Ref Arxiv: 1303.1921 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and are constructed via the Newton-Puiseux method. Then we study more carefully the case of monomial valuations and we give a result generalizing the Abhyankar-Jung Theorem for monic polynomials whose discriminant is weighted homogeneous. Commentaires: 63 pages