Hilbert's Tenth Problem for function fields of varieties over C
Number Theory
2007-05-23 v1
Abstract
Let K be the function field of a variety of dimension at least 2 over an algebraically closed field of characteristic zero. 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 C(t_1,t_2) is undecidable.
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Cite
@article{arxiv.math/0609540,
title = {Hilbert's Tenth Problem for function fields of varieties over C},
author = {Kirsten Eisentraeger},
journal= {arXiv preprint arXiv:math/0609540},
year = {2007}
}
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12 pages