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

Andrew Obus[1]

  • [1] University of Virginia 141 Cabell Drive Charlottesville, VA 22904

Journal de Théorie des Nombres de Bordeaux (2013)

  • Volume: 25, Issue: 3, page 579-633
  • ISSN: 1246-7405

Abstract

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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 ℚ ¯ , then the n th 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 .

How to cite

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Obus, Andrew. "Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II." Journal de Théorie des Nombres de Bordeaux 25.3 (2013): 579-633. <http://eudml.org/doc/275731>.

@article{Obus2013,
abstract = {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 $f: Y \rightarrow \{\mathbb\{P\}\}^1$ is a three-point $G$-Galois cover defined over $\overline\{\{\mathbb\{Q\}\}\}$, then the $n$th higher ramification groups above $p$ for the upper numbering of the (Galois closure of the) extension $K/\{\mathbb\{Q\}\}$ vanish, where $K$ is the field of moduli of $f$.},
affiliation = {University of Virginia 141 Cabell Drive Charlottesville, VA 22904},
author = {Obus, Andrew},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {field of moduli; stable reduction; Galois cover},
language = {eng},
month = {11},
number = {3},
pages = {579-633},
publisher = {Société Arithmétique de Bordeaux},
title = {Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II},
url = {http://eudml.org/doc/275731},
volume = {25},
year = {2013},
}

TY - JOUR
AU - Obus, Andrew
TI - Fields of moduli of three-point $G$-covers with cyclic $p$-Sylow, II
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2013/11//
PB - Société Arithmétique de Bordeaux
VL - 25
IS - 3
SP - 579
EP - 633
AB - 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 $f: Y \rightarrow {\mathbb{P}}^1$ is a three-point $G$-Galois cover defined over $\overline{{\mathbb{Q}}}$, then the $n$th higher ramification groups above $p$ for the upper numbering of the (Galois closure of the) extension $K/{\mathbb{Q}}$ vanish, where $K$ is the field of moduli of $f$.
LA - eng
KW - field of moduli; stable reduction; Galois cover
UR - http://eudml.org/doc/275731
ER -

References

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