Authors:	Javanpeykar, Ariyan Loughran, Daniel Mathur, Siddharth
Title:	Good reduction and cyclic covers
Online publication date:	27-Apr-2023
Year of first publication:	2022
Language:	english
Abstract:	We prove finiteness results for sets of varieties over number fields with good reduction outside a given finite set of places using cyclic covers. We obtain a version of the Shafarevich conjecture for weighted projective surfaces, double covers of abelian varieties and reduce the Shafarevich conjecture for hypersurfaces to the case of hypersurfaces of high dimension. These are special cases of a general setup for integral points on moduli stacks of cyclic covers, and our arithmetic results are achieved via a version of the Chevalley–Weil theorem for stacks.
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-8816
Version:	Published version
Publication type:	Zeitschriftenaufsatz
Document type specification:	Scientific article
License:	CC BY
Information on rights of use:	https://creativecommons.org/licenses/by/4.0/
Journal:	Journal of the Institute of Mathematics of Jussieu Version of Record (VoR)
Pages or article number:	1 32
Publisher:	Cambridge University Press
Publisher place:	Cambridge
Issue date:	2022
ISSN:	1475-3030
Publisher DOI:	10.1017/S1474748022000457
Appears in collections:	DFG-491381577-H