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

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

2010-01-21

arxiv.org/abs/1001.3723v5

Mathematics

Algebraic Geometry

Added Appendix A. Now 50 pages

Scientific paper

We continue the examination of the stable reduction and fields of moduli 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 P of order p^n. Suppose further that the normalizer of P acts on P via an involution. Under mild assumptions, if f: Y --> P^1 is a three-point G-Galois cover defined over C, 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.

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