Which invariants of a Galois -extension of local number fields (residue field of char , and Galois group ) determine the structure of the ideals in as modules over the group ring , the -adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups , we propose and study a new group (within the group ring where is the residue field) and its resulting ramification filtrations.
Quels invariants d’une -extension galoisienne de corps local (de corps résiduel de charactéristique et groupe de Galois ) déterminent la structure des idéaux de en tant que modules sur l’anneau de groupe , l’anneau des entiers -adiques ? Nous considérons cette question dans le cadre des extensions abéliennes élémentaires, bien que nous considérions aussi brièvement des extensions cycliques. Pour un groupe abélien élémentaire , nous proposons et étudions un nouveau groupe (dans l’anneau de groupe où est le corps résiduel) ainsi que ses filtrations de ramification.
@article{JTNB_2005__17_1_87_0, author = {Nigel P. Byott and G. Griffith Elder}, title = {New ramification breaks and additive {Galois} structure}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {87--107}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {1}, year = {2005}, doi = {10.5802/jtnb.479}, mrnumber = {2152213}, zbl = {1162.11394}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.479/} }
TY - JOUR AU - Nigel P. Byott AU - G. Griffith Elder TI - New ramification breaks and additive Galois structure JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 87 EP - 107 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.479/ DO - 10.5802/jtnb.479 LA - en ID - JTNB_2005__17_1_87_0 ER -
%0 Journal Article %A Nigel P. Byott %A G. Griffith Elder %T New ramification breaks and additive Galois structure %J Journal de théorie des nombres de Bordeaux %D 2005 %P 87-107 %V 17 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.479/ %R 10.5802/jtnb.479 %G en %F JTNB_2005__17_1_87_0
Nigel P. Byott; G. Griffith Elder. New ramification breaks and additive Galois structure. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 87-107. doi : 10.5802/jtnb.479. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.479/
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