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Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin

Guillaume Rond
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Abstract

We interpret the Artin-Rees lemma and the Izumi theorem in term of Artin function and we obtain a stable version of the Artin-Rees lemma. We present different applications of these interpretations. First we show that the Artin function of $X_1X_2-X_3X_4$, as a polynomial in the ring of power series in more than three variables, is not bounded by an affine function. Then we prove that the Artin functions of a class of polynomials are bounded by affine functions and we use this to compute approximated integral closures of ideals.

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Guillaume Rond. 2005-09-23. Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin. https://arxiv.org/abs/math/0502045

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