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

Cedric Luger

Abstract

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

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

Abstract

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

Paper Structure

This paper contains 2 theorems, 4 equations.

Key Result

Theorem 1

Let $k$ be a number field and let $X \to S$ be a morphism of normal integral projective $k$-varieties. Let $\Omega\subseteq S(k)$ be a subset that is not strongly thin in $S$ and such that, for every $s \in \Omega$, the fibre $X_s$ is a normal integral variety satisfying the Hilbert property over $k

Theorems & Definitions (6)

  • Definition 1
  • Definition 2
  • Definition 3
  • Theorem 1: Javanpeykar
  • Theorem 2
  • proof : Proof of Theorem \ref{['Thm:MixedFibration']}