Good reduction and cyclic covers

Ariyan Javanpeykar; Daniel Loughran; Siddharth Mathur

doi:10.1017/S1474748022000457

Good reduction and cyclic covers

Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	463-494
Number of pages	32
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	23
Issue number	1
Early online date	24 Oct 2022
DOIs	https://doi.org/10.1017/S1474748022000457
Publication status	Published - 31 Jan 2024

Funding

We thank David Rydh for many useful comments and suggestions. We are grateful to Jack Hall and Angelo Vistoli for helpful discussions, and Brian Lawrence and Will Sawin for help with the proof of Theorem . We thank the referee for helpful comments. The first named author gratefully acknowledges support of the IHES where part of this work was completed, as well as the University of Paris-Saclay for its hospitality. The second named author is supported by EPSRC grant EP/R021422/2. The third named author conducted this research in the framework of the research training group GRK 2240: Algebro-geometric Methods in Algebra, Arithmetic and Topology, which is funded by the Deutsche Forschungsgemeinschaft.

Funders	Funder number
Engineering and Physical Sciences Research Council	EP/R021422/2
Deutsche Forschungsgemeinschaft

Keywords

14G05 11G35 14D23

ASJC Scopus subject areas

General Mathematics

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10.1017/S1474748022000457Licence: CC BY

https://arxiv.org/abs/2009.01831

Cite this

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Good reduction and cyclic covers

Abstract

Funding

Keywords

ASJC Scopus subject areas

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Quantitative arithmetic geometry

Cite this

Good reduction and cyclic covers

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Quantitative arithmetic geometry

Cite this