Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q

Details Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of Q

2003-06-18

arxiv.org/abs/math/0306277v1

Mathematics

Number Theory

10 pages

Scientific paper

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.

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