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A negative solution to Hilbert's tenth problem for the ring of integers $O_F$of a number field $F$ would follow if $\mathbb{Z}$ 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 aconsequence of a well-known conjecture on elliptic surfaces.  --  Es sabido que se obtendr\'ia una soluci\'on negativa al d\'ecimo problema deHilbert para el anillo de enteros $O_F$ de un campo de n\'umeros $F$ si$\mathbb{Z}$ fuera diofantino en $O_F$. Denef y Lipshitz conjeturaron que esto\'ultimo ocurre para todo $F$. En esta nota se demuestra que la conjetura deDenef y Lipshitz es consecuencia de una conocida conjetura sobre superficiesel\'ipticas.

Superficies el\'ipticas y el d\'ecimo problema de Hilbert