Galois covers of the open p-adic disc

Details Galois covers of the open p-adic disc Galois covers of the open p-adic disc

2008-07-03

arxiv.org/abs/0807.0619v4

manuscripta math., 131, No. 1-2 (2010), 43-61

Mathematics

Number Theory

19 pages; substantial organizational and expository changes; this is the final version corresponding to the official publicati

Scientific paper

10.1007/s00229-009-0301-4

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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