Fields of moduli of threepoint Gcovers with cyclic pSylow, I
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 pSylow subgroup of order p^n. If G is further assumed to be psolvable (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 threepoint GGalois 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 threepoint Z/p^ncover, where p > 2.
 Publication:

arXiv eprints
 Pub Date:
 November 2009
 DOI:
 10.48550/arXiv.0911.1103
 arXiv:
 arXiv:0911.1103
 Bibcode:
 2009arXiv0911.1103O
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Number Theory;
 14G20;
 14H30 (Primary) 14H25;
 14G25;
 11G20;
 11S20 (Secondary)
 EPrint:
 Major reorganization. In particular, the former Appendix C has been spun off and is now arxiv:1109.4776. Now 42 pages