Division-ample sets and the Diophantine problem for rings of integers

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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.
9 pages, uses a4paper, calrsfs

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Number Theory, Logic, 03B25, 11U05

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http://salesiana.dossiersoluciones.com/handle/123456789/69660

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312382
 http://arxiv.org/abs/math/0312382

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arXiv