丢番图集的拓扑：关于Mazur猜想的注记
Topology of Diophantine Sets: Remarks on Mazur's Conjectures
摘要：
我们证明了Mazur关于簇上有理点的实拓扑的猜想意味着在有理数中不存在有理数的丢番图模型。证明了有限域上多项式环的丢番图模型存在于该有限域上的有理函数环中。这两个证明都依赖于Matijasevich定理。
英文摘要：
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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