Fields of moduli of three-point G-covers with cyclic p-Sylow, II
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, p. 579-633

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 1 is a three-point G-Galois cover defined over ¯, then the nth higher ramification groups above p for the upper numbering of the (Galois closure of the) extension K/ vanish, where K is the field of moduli of f.

Nous poursuivons l’étude de la réduction stable et des corps de modules des G-revêtements galoisiens de la droite projective sur un corps discrètement valué de caractéristique mixte (0,p), dans le cas où G a un p-sous-groupe de Sylow cyclique d’ordre p n . Supposons de plus que le normalisateur de P agit sur lui-même via une involution. Sous des hypothèses assez légères, nous montrons que si f:Y 1 est un G-revêtement galoisien ramifié au-dessus de 3 points, défini sur ¯, alors les n-ièmes groupes de ramification supérieure au-dessus de p, en numérotation supérieure, de (la clôture galoisienne de) l’extension K/ sont triviaux, où K est le corps des modules de f.

DOI : https://doi.org/10.5802/jtnb.850
Classification:  14G20,  11G22,  14H30,  14H25,  14G25,  11G20,  11S20
Keywords: field of moduli, stable reduction, Galois cover
@article{JTNB_2013__25_3_579_0,
     author = {Obus, Andrew},
     title = {Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {3},
     year = {2013},
     pages = {579-633},
     doi = {10.5802/jtnb.850},
     mrnumber = {3179678},
     zbl = {06291369},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2013__25_3_579_0}
}
Obus, Andrew. Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, pp. 579-633. doi : 10.5802/jtnb.850. http://www.numdam.org/item/JTNB_2013__25_3_579_0/

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