Hilbert’s Tenth Problem for function fields of varieties over algebraically closed fields of positive characteristic

摘要

Let K be the function field of a variety of dimension ≥ 2 over an algebraically closed field of odd characteristic. Then Hilbert’s Tenth Problem for K is undecidable. This generalizes the result by Kim and Roush from 1992 that Hilbert’s Tenth Problem for the purely transcendental function field ${{{overline{mathbb{F}}_p}}(t_1,t_2)}$ is undecidable when p 2.