Good reduction and cyclic covers

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2022

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Item type: Item , ZeitschriftenaufsatzAccess status: Open Access ,

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.

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http://doi.org/10.25358/openscience-8816

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https://openscience.ub.uni-mainz.de/handle/20.500.12030/8832

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Journal of the Institute of Mathematics of Jussieu, Version of Record (VoR), Cambridge University Press, Cambridge, 2022, https://doi.org/10.1017/S1474748022000457

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