Topology of Diophantine Sets: Remarks on Mazur's Conjectures

Details Topology of Diophantine Sets: Remarks on Mazur's Conjectures Topology of Diophantine Sets: Remarks on Mazur's Conjectures

2000-06-20

arxiv.org/abs/math/0006140v1

Mathematics

Logic

8 pages, uses ``amsart''

Scientific paper

We show that Mazur's conjecture on the real topology of rational points on
varieties implies that there is no diophantine model of the rational integers
in the rational numbers. We also prove that there is a diophantine model of the
polynomial ring over a finite field in the ring of rational functions over that
finite field. Both proofs depend upon Matijasevich's theorem.

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