Diophantine subsets of function fields of curves

Details Diophantine subsets of function fields of curves Diophantine subsets of function fields of curves

2007-08-25

arxiv.org/abs/0708.3451v2

Mathematics

Number Theory

Substantial revisions 1/18/08

Scientific paper

We consider diophantine subsets of function fields of curves and show,
roughly speaking, that they are either very small or very large. In particular,
this implies that the ring of polynomials $k[t]$ is a not a diophantine subset
of the field of rational functions $k(t)$ for many fields $k$.

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