2004/12/14 by Guillaume Rond, Rond, Guillaume
Mathematics · #03C10 (Primary) #11D75 #13B40 #14B12 #32B99 (Secondary) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #History and Theory of Mathematics #math.AC #msc:03C10 #msc:11D75 #msc:13B40 #msc:14B12 #msc:32B99
paper · pdf · doi:10.48550/arxiv.math/0412284
To appear in Ann. Sci. Ecole Norm. Sup., changes following referee's comments. Proofs have been improved and the counter-example can be read independantly from the first part
openalex publication_date 2004/12/14 · arxiv created 2005/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.