Autoren:	Corvaja, Pietro Demeio, Julian Lawrence Javanpeykar, Ariyan Lombardo, Davide Zannier, Umberto
Titel:	On the distribution of rational points on ramified covers of abelian varieties
Online-Publikationsdatum:	27-Apr-2023
Erscheinungsdatum:	2022
Sprache des Dokuments:	Englisch
Zusammenfassung/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-Sachgruppe:	510 Mathematik 510 Mathematics
Veröffentlichende Institution:	Johannes Gutenberg-Universität Mainz
Organisationseinheit:	FB 08 Physik, Mathematik u. Informatik
Veröffentlichungsort:	Mainz
ROR:	https://ror.org/023b0x485
DOI:	http://doi.org/10.25358/openscience-8814
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Weitere Angaben zur Dokumentart:	Scientific article
Nutzungsrechte:	CC BY
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by/4.0/
Zeitschrift:	Compositio Mathematica 158 11
Seitenzahl oder Artikelnummer:	2109 2155
Verlag:	Cambridge University Press
Verlagsort:	Cambridge
Erscheinungsdatum:	2022
ISSN:	1570-5846
DOI der Originalveröffentlichung:	10.1112/S0010437X22007746
Enthalten in den Sammlungen:	DFG-491381577-H