Good reduction and cyclic covers
Algebraic Geometry
2022-07-26 v3 Number Theory
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 set-up 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.
Cite
@article{arxiv.2009.01831,
title = {Good reduction and cyclic covers},
author = {Ariyan Javanpeykar and Daniel Loughran and Siddharth Mathur},
journal= {arXiv preprint arXiv:2009.01831},
year = {2022}
}
Comments
31 pages. Minor improvements and updated bibliography. Final version