Gutenberg Open Science: On the distribution of rational points on ramified covers of abelian varieties

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-8814

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DC Field	Value	Language
dc.contributor.author	Corvaja, Pietro	-
dc.contributor.author	Demeio, Julian Lawrence	-
dc.contributor.author	Javanpeykar, Ariyan	-
dc.contributor.author	Lombardo, Davide	-
dc.contributor.author	Zannier, Umberto	-
dc.date.accessioned	2023-04-27T12:43:23Z	-
dc.date.available	2023-04-27T12:43:23Z	-
dc.date.issued	2022	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/8830	-
dc.description.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.	en_GB
dc.language.iso	eng	de
dc.rights	CC BY	*
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	On the distribution of rational points on ramified covers of abelian varieties	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-8814	-
jgu.type.contenttype	Scientific article	de
jgu.type.dinitype	article	en_GB
jgu.type.version	Published version	de
jgu.type.resource	Text	de
jgu.organisation.department	FB 08 Physik, Mathematik u. Informatik	de
jgu.organisation.number	7940	-
jgu.organisation.name	Johannes Gutenberg-Universität Mainz	-
jgu.rights.accessrights	openAccess	-
jgu.journal.title	Compositio Mathematica	de
jgu.journal.volume	158	de
jgu.journal.issue	11	de
jgu.pages.start	2109	de
jgu.pages.end	2155	de
jgu.publisher.year	2022	-
jgu.publisher.name	Cambridge University Press	de
jgu.publisher.place	Cambridge	de
jgu.publisher.issn	1570-5846	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1112/S0010437X22007746	de
jgu.organisation.ror	https://ror.org/023b0x485	-
jgu.subject.dfg	Naturwissenschaften	de
Appears in collections:	DFG-491381577-H

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