New ramification breaks and additive Galois structure
Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 87-107.

Which invariants of a Galois p-extension of local number fields L/K (residue field of char p, and Galois group G) determine the structure of the ideals in L as modules over the group ring p [G], p the p-adic integers? We consider this question within the context of elementary abelian extensions, though we also briefly consider cyclic extensions. For elementary abelian groups G, we propose and study a new group (within the group ring 𝔽 q [G] where 𝔽 q is the residue field) and its resulting ramification filtrations.

Quels invariants d’une p-extension galoisienne de corps local L/K (de corps résiduel de charactéristique p et groupe de Galois G) déterminent la structure des idéaux de L en tant que modules sur l’anneau de groupe p [G], p l’anneau des entiers p-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 G, nous proposons et étudions un nouveau groupe (dans l’anneau de groupe 𝔽 q [G]𝔽 q est le corps résiduel) ainsi que ses filtrations de ramification.

DOI: 10.5802/jtnb.479
Nigel P. Byott 1; G. Griffith Elder 2

1 Department of Mathematical Sciences University of Exeter Exeter EX4 4QE United Kingdom
2 Department of Mathematics University of Nebraska at Omaha Omaha, NE 68182-0243 U.S.A.
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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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