Autoren:	Javanpeykar, Ariyan Levin, Aaron
Titel:	Urata's theorem in the logarithmic case and applications to integral points
Online-Publikationsdatum:	2-Feb-2023
Erscheinungsdatum:	2022
Sprache des Dokuments:	Englisch
Zusammenfassung/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.
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-8759
Version:	Published version
Publikationstyp:	Zeitschriftenaufsatz
Weitere Angaben zur Dokumentart:	Scientific article
Nutzungsrechte:	CC BY-NC-ND
Informationen zu den Nutzungsrechten:	https://creativecommons.org/licenses/by-nc-nd/4.0/
Zeitschrift:	Bulletin of the London Mathematical Society 54 5
Seitenzahl oder Artikelnummer:	1772 1790
Verlag:	John Wiley & Sons, Ltd
Verlagsort:	Oxford
Erscheinungsdatum:	2022
ISSN:	1469-2120
DOI der Originalveröffentlichung:	10.1112/blms.12655
Enthalten in den Sammlungen:	DFG-491381577-H