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

2005/02/02 by Guillaume Rond, Rond, Guillaume
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.math/0502045

to appear in J. of Algebra; a lot of misprints changed and some proofs are improved following referee's comments

arxiv created 2005/09/23 · arxiv updated 2009/12/01

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 X₁X₂-X₃X₄, 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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