Division-ample sets and the Diophantine problem for rings of integers
Number Theory
2007-05-23 v1 Logic
Abstract
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division-ample set of integers and of an elliptic curve of rank one over K). We relate division-ample sets to arithmetic of abelian varieties.
Cite
@article{arxiv.math/0312382,
title = {Division-ample sets and the Diophantine problem for rings of integers},
author = {Gunther Cornelissen and Thanases Pheidas and Karim Zahidi},
journal= {arXiv preprint arXiv:math/0312382},
year = {2007}
}
Comments
9 pages, uses a4paper, calrsfs