Authors:	Javanpeykar, Ariyan
Title:	Arithmetic hyperbolicity: automorphisms and persistence
Online publication date:	4-Jul-2022
Year of first publication:	2021
Language:	english
Abstract:	We show that if the automorphism group of a projective variety is torsion, then it is finite. Motivated by Lang’s conjecture on rational points of hyperbolic varieties, we use this to prove that a projective variety with only finitely many rational points has only finitely many automorphisms. Moreover, we investigate to what extent finiteness of S-integral points on a variety over a number field persists over finitely generated fields. To this end, we introduce the class of mildly bounded varieties and prove a general criterion for proving this persistence.
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-7280
Version:	Published version
Publication type:	Zeitschriftenaufsatz
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Mathematische Annalen 381
Pages or article number:	439 457
Publisher:	Springer
Publisher place:	Berlin u.a.
Issue date:	2021
ISSN:	1432-1807
Publisher DOI:	10.1007/s00208-021-02155-0
Appears in collections:	JGU-Publikationen