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Fields of moduli of three-point G-covers with cyclic p-Sylow, I

Authors
  • Obus, Andrew
Type
Published Article
Publication Date
Sep 26, 2011
Submission Date
Nov 05, 2009
Source
arXiv
License
Yellow
External links

Abstract

We examine in detail the stable reduction of Galois covers of the projective line over a complete discrete valuation field of mixed characteristic (0, p), where G has a cyclic p-Sylow subgroup of order p^n. If G is further assumed to be p-solvable (i.e., G has no nonabelian simple composition factors with order divisible by p), we obtain the following consequence: Suppose f: Y --> P^1 is a three-point G-Galois cover defined over the complex numbers. Then the nth higher ramification groups above p for the upper numbering of the (Galois closure of the) extension K/Q vanish, where K is the field of moduli of f. This extends work of Beckmann and Wewers. Additionally, we completely describe the stable model of a general three-point Z/p^n-cover, where p > 2.

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