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Article Dans Une Revue Journal of Algebra Année : 2012

The Abhyankar–Jung Theorem

Résumé

We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \in \K[[X]][Z] $, $X=(X_1,..., X_n)$, over an algebraically closed field of characterisic zero $\K$, and satisfying $a_1=0$, is $\nu$-quasi-ordinary. That means that if the discriminant $\Delta_P \in \K[[X]]$ is equal to a monomial times a unit then the ideal $(a_i^{d!/i}(X))_{i=2,...,d}$ is principal and generated by a monomial. 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.

Dates et versions

hal-00941003 , version 1 (03-02-2014)

Identifiants

Citer

Adam Parusiński, Guillaume Rond. The Abhyankar–Jung Theorem. Journal of Algebra, 2012, 365, pp.29 - 41. ⟨10.1016/j.jalgebra.2012.05.003⟩. ⟨hal-00941003⟩
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