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Sur la linearite de la fonction de Artin

Research paper by Guillaume Rond

Indexed on: 25 Oct '05Published on: 25 Oct '05Published in: Mathematics - Commutative Algebra



Abstract

We give here a counter-example to a conjecture of Spivakovsky. M. Spivakovsky conjectured that the function that appears in the strong Artin approximation theorem is bounded by a linear function. First we show that there is no Liouville theorem for the field of fractions of the ring of power series in several variables. We deduce from this example that there is no theory of elimination of quantifiers for the field of fractions of the ring of power series in several variables.