GOOD REDUCTION AND CYCLIC COVERS

Author:

Javanpeykar AriyanORCID,Loughran Daniel,Mathur Siddharth

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference51 articles.

1. Hypersurfaces of low degree

2. Almost proper GIT-stacks and discriminant avoidance;Starr;Doc. Math.,2010

3. Algebraic geometry I. Schemes–with examples and exercises;Görtz;Springer Studium Mathematik–Master

4. A variational Torelli theorem for cyclic coverings of high degree;Ivinskis;Compositio Math.,1993

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