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Galois covers of the open p-adic disc

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Abstract

This paper investigates Galois branched covers of the open p-adic disc and their reductions to characteristic p. Using the field of norms functor of Fontaine and Wintenberger, we show that the special fiber of a Galois cover is determined by arithmetic and geometric properties of the generic fiber and its characteristic zero specializations. As applications, we derive a criterion for good reduction in the abelian case, and give an arithmetic reformulation of the local Oort Conjecture concerning the liftability of cyclic covers of germs of curves.

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  1. Department of Mathematics, Lawrence University, 711 E. Boldt Way, Appleton, WI, 54911, USA

    Scott Corry

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  1. Scott Corry
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Correspondence to Scott Corry.

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Corry, S. Galois covers of the open p-adic disc. manuscripta math. 131, 43–61 (2010). https://doi.org/10.1007/s00229-009-0301-4

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  • DOI: https://doi.org/10.1007/s00229-009-0301-4

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