The Abhyankar-jung Theorem
نویسندگان
چکیده
We show that every quasi-ordinary Weierstrass polynomial P (Z) = Z + a1(X)Z d−1 + · · ·+ ad(X) ∈ K[[X]][Z], X = (X1, . . . , Xn), over an algebraically closed field of characterisic zero K, such that a1 = 0, is ν-quasi-ordinary. That means that if the discriminant ∆P ∈ K[[X]] is equal to a monomial times a unit then the ideal (a i (X))i=2,...,d is monomial and generated by one of a i (X). We use this result to give a constructive proof of the Abhyankar-Jung Theorem that works for any Henselian local subring of K[[X]] and the function germs of quasi-analytic families.
منابع مشابه
The Abhyankar–Jung theorem for excellent henselian subrings of formal power series
Given an algebraically closed field K of characteristic zero, we present the Abhyankar–Jung theorem for any excellent henselian ring whose completion is a formal power series ring K[[z]]. In particular, examples include the local rings which form a Weierstrass system over the field K. The Abhyankar–Jung theorem may be regarded as a higher dimensional counterpart of the Newton–Puiseux theorem. I...
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