A mixed fibration theorem for Hilbert irreducibility on non-proper varieties

TL;DR

This paper proves that the weak Hilbert property can be transferred along certain morphisms between varieties over fields of characteristic zero, broadening understanding of Hilbert irreducibility in algebraic geometry.

Contribution

It introduces a mixed fibration theorem that extends the weak Hilbert property to non-proper varieties under specific conditions.

Findings

Weak Hilbert property ascends along morphisms.

Applicable to non-proper varieties over characteristic zero fields.

Provides new tools for studying Hilbert irreducibility.

Abstract

We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.