Good reduction and cyclic covers

Ariyan Javanpeykar, Daniel Loughran, Siddharth Mathur

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)463-494
JournalJournal of the Institute of Mathematics of Jussieu
Volume23
Issue number1
Early online date24 Oct 2022
DOIs
Publication statusPublished - 31 Jan 2024

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