Gutenberg Open Science: Urata's theorem in the logarithmic case and applications to integral points

Please use this identifier to cite or link to this item: http://doi.org/10.25358/openscience-8759

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DC Field	Value	Language
dc.contributor.author	Javanpeykar, Ariyan	-
dc.contributor.author	Levin, Aaron	-
dc.date.accessioned	2023-02-02T11:15:56Z	-
dc.date.available	2023-02-02T11:15:56Z	-
dc.date.issued	2022	-
dc.identifier.uri	https://openscience.ub.uni-mainz.de/handle/20.500.12030/8775	-
dc.description.abstract	Urata showed that a pointed compact hyperbolic variety admits only finitely many maps from a pointed curve. We extend Urata’s theorem to the setting of (not necessarily compact) hyperbolically embeddable varieties. As an application, we show that a hyperbolically embeddable variety over a number field 𝐾 with only finitely many𝐿,𝑇-points for any number field 𝐿∕𝐾and any finite set of finite places 𝑇 of 𝐿 has, in fact, only finitely many points in any given ℤ-finitely generated integral domain of characteristic zero. We use this latter result in combination with Green’s criterion for hyperbolic embeddability to obtain novel finiteness results for integral points on symmetric self-products of smooth affine curves and on complements of large divisors in projective varieties. Finally, we use a partial converse to Green’s criterion to further study hyperbolic embeddability (or its failure) in the case of symmetric self-products of curves. As a by-product of our results, we obtain the first example of a smooth affine Brody-hyperbolic threefold over ℂ which is not hyperbolically embeddable.	en_GB
dc.description.sponsorship	Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) – Projektnummer 491381577	de
dc.language.iso	eng	de
dc.rights	CC BY-NC-ND	*
dc.rights.uri	https://creativecommons.org/licenses/by-nc-nd/4.0/	*
dc.subject.ddc	510 Mathematik	de_DE
dc.subject.ddc	510 Mathematics	en_GB
dc.title	Urata's theorem in the logarithmic case and applications to integral points	en_GB
dc.type	Zeitschriftenaufsatz	de
dc.identifier.doi	http://doi.org/10.25358/openscience-8759	-
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	Bulletin of the London Mathematical Society	de
jgu.journal.volume	54	de
jgu.journal.issue	5	de
jgu.pages.start	1772	de
jgu.pages.end	1790	de
jgu.publisher.year	2022	-
jgu.publisher.name	John Wiley & Sons, Ltd	de
jgu.publisher.place	Oxford	de
jgu.publisher.issn	1469-2120	de
jgu.organisation.place	Mainz	-
jgu.subject.ddccode	510	de
jgu.publisher.doi	10.1112/blms.12655	de
jgu.organisation.ror	https://ror.org/023b0x485	-
jgu.subject.dfg	Naturwissenschaften	de
Appears in collections:	DFG-491381577-H

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