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Hilbert's irreducibility theorem for abelian varieties

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

Indexed on: 26 Nov '20Published on: 25 Nov '20Published in: arXiv - Mathematics - Number Theory



Abstract

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.