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On relative computability for curves

Minhyong Kim
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Abstract

We discuss a rational version of a conjecture of Matiyasevich, Davis, and Putnam on the relative decidability of the finiteness problem for Diophantine equations with respect to the existence problem. We formulate a suspicion that for rational solutions, the finiteness problem should be relatively decidable in contrast to the M-D-P conjecture for integer solutions.

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Minhyong Kim. 2005-02-10. On relative computability for curves. https://arxiv.org/abs/math/0502224

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