Geodesic
Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of ℚ
Poonen, Bjorn1
1Department of Mathematics, University of California, Berkeley, California 94720-3840
Journal of the American Mathematical Society, Tome 16 (2003) no. 4, pp. 981-990

Voir la notice de l'article provenant de la source American Mathematical Society

We give the first examples of infinite sets of primes $S$ such that Hilbert’s Tenth Problem over $\mathbb {Z}[S^{-1}]$ 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 $\mathbb {Z}[S^{-1}]$ such that the topological closure of $E’(\mathbb {Z}[S^{-1}])$ in $E’(\mathbb {R})$ has infinitely many connected components.
DOI : 10.1090/S0894-0347-03-00433-8

Poonen, Bjorn  1

1 Department of Mathematics, University of California, Berkeley, California 94720-3840 
Poonen, Bjorn. Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of ℚ. Journal of the American Mathematical Society, Tome 16 (2003) no. 4, pp. 981-990. doi: 10.1090/S0894-0347-03-00433-8
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