Diophantine inequality for equicharacteristic excellent Henselian local domains

TL;DR

This paper extends a Diophantine inequality originally proved for power series fields to a broader class of fields arising from excellent Henselian local domains in equicharacteristic, enhancing understanding of their algebraic properties.

Contribution

The paper generalizes Rond's Diophantine inequality to fields of quotients of excellent Henselian local domains in equicharacteristic, broadening its applicability.

Findings

Generalization of Diophantine inequality to new algebraic structures

Broader understanding of field properties in algebraic geometry

Potential implications for local uniformization

Abstract

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.