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Approximation of Holomorphic Solutions of a System of Real Analytic Equations

  Published:2011-06-29
 Printed: Dec 2012
  • M. Hickel,
    Université Bordeaux 1, I.M.B., Equipe d'Analyse et Géométrie, et I.U.T. Bordeaux 1 département Informatique, 33405 Talence Cedex, France
  • G. Rond,
    I.M.L. Faculté des Sciences de Luminy, Case 907, 163 av. de Luminy, 13288 Marseille Cedex 9, France
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Abstract

We prove the existence of an approximation function for holomorphic solutions of a system of real analytic equations. For this we use ultraproducts and Weierstrass systems introduced by J. Denef and L. Lipshitz. We also prove a version of the Płoski smoothing theorem in this case.
Keywords: Artin approximation, real analytic equations Artin approximation, real analytic equations
MSC Classifications: 13B40, 13L05, 14F12 show english descriptions Etale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
unknown classification 14F12
13B40 - Etale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25]
13L05 - Applications of logic to commutative algebra [See also 03Cxx, 03Hxx]
14F12 - unknown classification 14F12
 

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