Submission date: 22 March 2024

Abstract:

We study model-complete fields that avoid a given quasi-project variety V. There is a close connection between hyperbolicity of V and the existence of the model companion for the theory of characteristic-zero fields without rational points on V, extending the results for curves by Will Johnson and Jinhe Ye. In particular, we show that if V is a Brody hyperbolic projective variety over ℚ with V(ℚ) = ∅, then the model companion, called VXF, exists. We also study some model-theoretic properties of VXF.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2403.15300: pdf, ps.