Authors:	Corvaja, Pietro Demeio, Julian Lawrence Javanpeykar, Ariyan Lombardo, Davide Zannier, Umberto
Title:	On the distribution of rational points on ramified covers of abelian varieties
Online publication date:	27-Apr-2023
Year of first publication:	2022
Language:	english
Abstract:	We prove new results on the distribution of rational points on ramified covers of abelian varieties over finitely generated fields k of characteristic zero. For example, given a ramified cover π:X→A, where A is an abelian variety over k with a dense set of k-rational points, we prove that there is a finite-index coset C⊂A(k) such that π(X(k)) is disjoint from C. Our results do not seem to be in the range of other methods available at present; they confirm predictions coming from Lang's conjectures on rational points, and also go in the direction of an issue raised by Serre regarding possible applications to the inverse Galois problem. Finally, the conclusions of our work may be seen as a sharp version of Hilbert's irreducibility theorem for abelian varieties.
DDC:	510 Mathematik 510 Mathematics
Institution:	Johannes Gutenberg-Universität Mainz
Department:	FB 08 Physik, Mathematik u. Informatik
Place:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-8814
Version:	Published version
Publication type:	Zeitschriftenaufsatz
Document type specification:	Scientific article
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Compositio Mathematica 158 11
Pages or article number:	2109 2155
Publisher:	Cambridge University Press
Publisher place:	Cambridge
Issue date:	2022
ISSN:	1570-5846
Publisher DOI:	10.1112/S0010437X22007746
Appears in collections:	DFG-491381577-H