This paper provides a complete catalog of the break numbers that occur in the ramification filtration of fully and thus wildly ramified quaternion extensions of dyadic number fields which contain (along with some partial results for the more general case). This catalog depends upon the refined ramification filtration, which as defined in [2] is associated with the biquadratic subfield. Moreover we find that quaternion counter-examples to the conclusion of the Hasse-Arf Theorem are extremely rare and can occur only when the refined ramification filtration is, in two different ways, extreme.
Cet article fournit un catalogue complet des nombres de ramification qui se produisent dans la filtration de ramification des extensions totalement ramifiées des corps de nombres dyadiques qui contiennent , et dont le groupe Galois est isomorphe au groupe des quaternions (avec quelques résultats partiels dans le cas plus général). Ce catalogue dépend d’un rafinement de la filtration de ramification. Cette filtration était definie dans [2] comme associée au sous-corps biquadratique. En outre, nous montrons que les contre-exemples de type quaternion aux conclusions du théorème de Hasse-Arf sont extrêmement rares et ne peuvent se produire que seulement dans le cas où la filtration raffinée de ramification est extrême dans deux directions distinctes.
@article{JTNB_2007__19_1_101_0, author = {Elder, G. Griffith and Hooper, Jeffrey J.}, title = {On wild ramification in quaternion extensions}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {101--124}, publisher = {Universit\'e Bordeaux 1}, volume = {19}, number = {1}, year = {2007}, doi = {10.5802/jtnb.576}, zbl = {1123.11037}, mrnumber = {2332056}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/jtnb.576/} }
TY - JOUR AU - Elder, G. Griffith AU - Hooper, Jeffrey J. TI - On wild ramification in quaternion extensions JO - Journal de théorie des nombres de Bordeaux PY - 2007 SP - 101 EP - 124 VL - 19 IS - 1 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/10.5802/jtnb.576/ DO - 10.5802/jtnb.576 LA - en ID - JTNB_2007__19_1_101_0 ER -
%0 Journal Article %A Elder, G. Griffith %A Hooper, Jeffrey J. %T On wild ramification in quaternion extensions %J Journal de théorie des nombres de Bordeaux %D 2007 %P 101-124 %V 19 %N 1 %I Université Bordeaux 1 %U http://archive.numdam.org/articles/10.5802/jtnb.576/ %R 10.5802/jtnb.576 %G en %F JTNB_2007__19_1_101_0
Elder, G. Griffith; Hooper, Jeffrey J. On wild ramification in quaternion extensions. Journal de théorie des nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 101-124. doi : 10.5802/jtnb.576. http://archive.numdam.org/articles/10.5802/jtnb.576/
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