About the Algebraic Closure of the Field of Power Series in Several Variables in Characteristic Zero
نویسنده
چکیده
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. Essentially this result asserts that the Galois group of such a polynomial is isomorphic to the Galois group of one weighted homogeneous polynomial.
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