Hilbert irreducibility for abelian varieties over function fields of characteristic zero

TL;DR

This paper proves a version of Hilbert's irreducibility theorem specifically for abelian varieties over function fields of characteristic zero, expanding the understanding of their arithmetic properties.

Contribution

It establishes Hilbert's irreducibility theorem in the context of abelian varieties over characteristic zero function fields, a novel extension of classical results.

Findings

Hilbert's irreducibility holds for abelian varieties over these fields.

The result broadens the scope of irreducibility theorems in algebraic geometry.

Implications for the arithmetic of abelian varieties are discussed.

Abstract

We prove Hilbert's irreducibility theorem for abelian varieties over function fields of characteristic zero.