Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q
Number Theory
2017-04-03 v1 Logic
Abstract
We give the first examples of infinite sets of primes S such that Hilbert's Tenth Problem over Z[S^{-1}] has a negative answer. In fact, we can take S to be a density 1 set of primes. We show also that for some such S there is a punctured elliptic curve E' over Z[S^{-1}] such that the topological closure of E'(Z[S^{-1}]) in E'(R) has infinitely many connected components.
Keywords
Cite
@article{arxiv.math/0306277,
title = {Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:math/0306277},
year = {2017}
}
Comments
10 pages