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arXiv · 0807.0619

Galois covers of the open p-adic disc

Scott Corry
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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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Scott Corry. 2011-03-08. Galois covers of the open p-adic disc. https://doi.org/10.1007/s00229-009-0301-4

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