Abstract

PASTEN, Hector. Elliptic surfaces and Hilbert’s tenth problem. Rev. Mat [online]. 2023, vol.30, n.1, pp.113-120. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v30i1.52266.

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.

Keywords : Hilbert’s tenth problem; rings of integers; elliptic surfaces; elliptic curves..

        · abstract in Spanish     · text in Spanish     · Spanish ( pdf )