Submission date: 24 August 2022

Abstract:

It is an old problem in the area of Diophantine definability to determine whether ℚ is Diophantine in ℚ(z). We provide a positive answer conditional on two standard conjectures on elliptic surfaces.

Mathematics Subject Classification: 11U09, Secondary: 14J27, 11G05

Keywords and phrases:

Full text arXiv 2208.11616: pdf, ps.