Vol. 6, No. 5, 2012

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

Andrew Obus

Vol. 6 (2012), No. 5, 833–883

We examine in detail the stable reduction of G-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 pn. If G is further assumed to be p-solvable (that is, G has no nonabelian simple composition factors with order divisible by p), we obtain the following consequence: Suppose f : Y 1 is a three-point G-Galois cover defined over . Then the n-th higher ramification groups above p for the upper numbering for the extension K 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 pn-cover, where p > 2.

Field of moduli, stable reduction, Galois cover
Mathematical Subject Classification 2000
Primary: 14H30
Secondary: 14G20, 14G25, 14H25, 11G20, 11S20
Received: 9 December 2009
Revised: 22 September 2011
Accepted: 4 November 2011
Published: 31 July 2012
Andrew Obus
Columbia University
Department of Mathematics
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New York, NY 10027
United States