|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
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