Diophantine Maps

A. Eggink

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arXiv · 2409.18845

Diophantine Maps

A. Eggink

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Abstract

To prove that Hilbert's tenth problem over a ring R has a negative answer, usually the integers or another ring for which Hilbert's tenth problem has a negative solution is modelled inside the ring of interest. In this paper, we formalize this practice by introducing the notions of a Diophantine map and a Diophantine equivalence map. We compare the Diophantine case to the recursive case. We formalize a general version of Hilbert's tenth problem and show that we can transfer a positive or negative answer to Hilbert's tenth problem using effective Diophantine maps.

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A. Eggink. 2024-09-27. Diophantine Maps. https://arxiv.org/abs/2409.18845

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