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James Weigandt
James Weigandt
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I'm a little new to this stuff so I might not know exactly what you're asking.

I believe there is a conjecture of Mazur that implies the type of description of $\Bbb Z$ you are looking for is impossible.

This paper by Poonen would be a good place to start. Of course Poonen would be able to give a much more satisfying answer. I only caught the end of his talk about this stuff at the Joint Meetings.

EDIT:

Here Cornelissen and Zahidi show that Mazur's conjecture on the real topology of rational points on varieties implies that there is no diophantine model of $\Bbb Z$ over $\Bbb Q$. They also show that the analogue of Mazur's conjecture is false in the function field case, where Hilbert's Tenth has a negative answer.

I'm a little new to this stuff so I might not know exactly what you're asking.

I believe there is a conjecture of Mazur that implies the type of description of $\Bbb Z$ you are looking for is impossible.

This paper by Poonen would be a good place to start. Of course Poonen would be able to give a much more satisfying answer. I caught the end of his talk about this stuff at the Joint Meetings.

I'm a little new to this stuff so I might not know exactly what you're asking.

I believe there is a conjecture of Mazur that implies the type of description of $\Bbb Z$ you are looking for is impossible.

This paper by Poonen would be a good place to start. Of course Poonen would be able to give a much more satisfying answer. I only caught the end of his talk about this stuff at the Joint Meetings.

EDIT:

Here Cornelissen and Zahidi show that Mazur's conjecture on the real topology of rational points on varieties implies that there is no diophantine model of $\Bbb Z$ over $\Bbb Q$. They also show that the analogue of Mazur's conjecture is false in the function field case, where Hilbert's Tenth has a negative answer.

Source Link
James Weigandt
James Weigandt
  • 3.3k
  • 1
  • 31
  • 36

I'm a little new to this stuff so I might not know exactly what you're asking.

I believe there is a conjecture of Mazur that implies the type of description of $\Bbb Z$ you are looking for is impossible.

This paper by Poonen would be a good place to start. Of course Poonen would be able to give a much more satisfying answer. I caught the end of his talk about this stuff at the Joint Meetings.