Paper detail

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

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.