Keywords
Anillos de enteros
Superficies elípticas
Curvas elípticas
Hilbert’s tenth problem
Rings of integers
Elliptic surfaces
Elliptic curves
How to Cite
Abstract
A negative solution to Hilbert’s tenth problem for the ring of integers OF of a number field F would follow if Z were Diophantine in OF. 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.
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