Fields of moduli of three-point G-covers with cyclic p-Sylow, 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 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.
- Publication:
-
arXiv e-prints
- 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)
- E-Print:
- Major reorganization. In particular, the former Appendix C has been spun off and is now arxiv:1109.4776. Now 42 pages