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Preprint Number 2217

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2217. Hector Pasten
Superficies elípticas y el décimo problema de Hilbert

Submission date: 20 July 2022


In Spanish

A negative solution to Hilbert's tenth problem for the ring of integers O_F of a number field F would follow if ℤ were Diophantine in O_F. Denef and Lipshitz conjectured that the latter occurs for every number field F. In this note we show that the conjecture of Denef and Lipshitz is a consequence of a well-known conjecture on elliptic surfaces.

Es sabido que se obtendría una solución negativa al décimo problema de Hilbert para el anillo de enteros O_F de un campo de números F si ℤ fuera diofantino en O_F. Denef y Lipshitz conjeturaron que esto último ocurre para todo F. En esta nota se demuestra que la conjetura de Denef y Lipshitz es consecuencia de una conocida conjetura sobre superficies elípticas.

Mathematics Subject Classification: Primary: 11U05, Secondary: 14J27, 11G05

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Full text arXiv 2207.10005: pdf, ps.

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