Year: 2025
Type: article
Abstract: : Assuming the weak Bombieri-Lang conjecture, we prove that a generalization of Hilbert’s irreducibility theorem holds for families of geometrically mordellic varieties (for instance, families of hyperbolic curves). As an application we prove that, assuming Bombieri-Lang, there are no polynomial bijections $\Q\times\Q\to\Q$, completing a strategy originally suggested by T. Tao.
Source: American Journal of Mathematics
Author: Giulio Bresciani
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4410922150