Diophantine inequality for equicharacteristic excellent Henselian local domains

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (2) 2008, pp. 48–55

June 30, 2008

Hirotada Ito, Interdisciplinary Graduate School of Science and Engineering, Kinki University, Higashi-Osaka 577-8502, Japan; email: reen.salt.7125-8753@s6.dion.ne.jp

Shuzo Izumi, Department of Mathematics, Kinki University, Higashi-Osaka 577-8502, Japan; email: sizmsizm@gmail.com

Abstract/Résumé:

G. Rond has proved a Diophantine type inequality for the field of quotients of the convergent or formal power series ring in multivariables. We generalize his theorem to the field of the quotients of an excellent Henselian local domain in equicharacteristic case.

G. Rond a démontré une inégalité de type diophantien pour le corps des quotients de séries convergentes (ou formelles) à plusieurs variables. On fait ici une généralisation de son théorème au corps des quotients d’un anneau local intégral henselien excellent dans le cas équi-caractéristique.

Keywords: Diophantine inequality, associated valuations, linear Artin approximation property, m-valuation
AMS Subject Classification: Valuation rings 13F30

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