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

Guillaume Rond (1)

1 LEP - Laboratoire Émile Picard

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.

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]

Guillaume Rond. Lemme d'Artin-Rees, theoreme d'Izumi et fonction de Artin. Journal of Algebra, 2006, 299, pp.245-275. ⟨hal-00125565⟩