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arXiv · 1303.1921

About the algebraic closure of the field of power series in several variables in characteristic zero

Guillaume Rond
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Abstract

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.

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Guillaume Rond. 2013-03-08. About the algebraic closure of the field of power series in several variables in characteristic zero. https://arxiv.org/abs/1303.1921

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