Diophantine approximation in fields of power series in several variables

Guillaume Rond[1]

  • [1] University of Toronto Department of Mathematics Toronto, Ontario M5S 2E4 (Canada)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 2, page 299-308
  • ISSN: 0373-0956

Abstract

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We prove a theorem of diophantine approximation between the field of formal power series in several variables and its completion for the Krull topology.

How to cite

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Rond, Guillaume. "Approximation diophantienne dans les corps de séries en plusieurs variables." Annales de l’institut Fourier 56.2 (2006): 299-308. <http://eudml.org/doc/10146>.

@article{Rond2006,
abstract = {Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.},
affiliation = {University of Toronto Department of Mathematics Toronto, Ontario M5S 2E4 (Canada)},
author = {Rond, Guillaume},
journal = {Annales de l’institut Fourier},
keywords = {approximation diophantienne; approximation de Artin; fonction de Artin},
language = {fre},
number = {2},
pages = {299-308},
publisher = {Association des Annales de l’institut Fourier},
title = {Approximation diophantienne dans les corps de séries en plusieurs variables},
url = {http://eudml.org/doc/10146},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Rond, Guillaume
TI - Approximation diophantienne dans les corps de séries en plusieurs variables
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 2
SP - 299
EP - 308
AB - Nous montrons ici un théorème d’approximation diophantienne entre le corps des séries formelles en plusieurs variables et son complété pour la topologie de Krull.
LA - fre
KW - approximation diophantienne; approximation de Artin; fonction de Artin
UR - http://eudml.org/doc/10146
ER -

References

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  1. M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES 36 (1969), 23-58 Zbl0181.48802MR268188
  2. M. J. Greenberg, Rational points in henselian discrete valuation rings, Publ. Math. IHES 31 (1966), 59-64 Zbl0146.42201MR207700
  3. M. Hickel, Calcul de la fonction d’Artin-Greenberg d’une branche plane, Pacific J. of Math. 213 (2004), 37-47 Zbl1054.14036MR2040249
  4. S. Izumi, A measure of integrity for local analytic algebras, Publ. RIMS, Kyoto Univ. 21 (1985), 719-736 Zbl0587.32016MR817161
  5. A. Lasjaunias, A survey of Diophantine approximation in fields of power series, Monatsh. Math. 130 (2000), 211-229 Zbl0990.11043MR1777096
  6. M. Lejeune-Jalabert, Arcs analytiques et résolution minimales des singularités des surfaces quasihomogènes, Lectures Notes in Math. 777 (1980), 303-336 Zbl0432.14020
  7. J. Nash, Arcs structure of singularities, Duke Math. J. 81 (1995), 31-38 Zbl0880.14010MR1381967
  8. D. Rees, Izumi’s theorem, Commutative algebra, Math. Sci. Res. Inst. Publ. 15 (1989), 407-416 Zbl0741.13011MR1015531
  9. A. Reguera, Image of the Nash map in terms of wedges, C. R. Math. Acad. Sci. Paris 338 (2004), 385-390 Zbl1044.14032MR2057169
  10. G. Rond, Sur la linéarité de la fonction de Artin, (2006) Zbl1109.14006
  11. J.-C. Tougeron, Idéaux de fonctions différentiables, Ergebnisse der Mathematik und ihrer Grenzgebiete 71 (1972) Zbl0251.58001MR440598
  12. J. J. Wavrik, A theorem on solutions of analytic equations with applications to deformations of complex structures, Math. Ann. 216 (1975), 127-142 Zbl0303.32018MR387649

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