Hilbert's irreducibility theorem for abelian varieties

Pietro Corvaja, Julian Lawrence Demeio, Ariyan Javanpeykar, Davide Lombardo, Umberto Zannier

Published 2020-11-25Version 1

We prove a version of Hilbert's irreducibility theorem for abelian varieties over finitely generated fields of characteristic zero, thereby generalizing earlier results of Zannier for powers of non-CM elliptic curves. Our work proves a conjecture of Corvaja-Zannier on varieties with many rational points in the case of abelian varieties, and confirms predictions made by Lang's conjecture on rational points.