Hilbert's Tenth Problem for function fields of varieties over C

Details Hilbert's Tenth Problem for function fields of varieties over C Hilbert's Tenth Problem for function fields of varieties over C

2006-09-20

arxiv.org/abs/math/0609540v1

Int. Math. Res. Not. 59 (2004), 3191-3205

Mathematics

Number Theory

12 pages

Scientific paper

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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