Stability of the Kato-Kuzumaki's properties under field extensions
Abstract
In 1986, Kato and Kuzumaki introduced some Diophantine properties of fields, called the Ciq properties, and they hoped they would provide a good characterization of the cohomological dimension of fields. In this paper, we study the stability of some variants of the Ciq properties under transcendental and algebraic extensions. As an application, we obtain the Cn1 property for the field Fp(x1,·s,xn).
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