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New ramification breaks and additive Galois structure

Nigel P. Byott, G. Griffith Elder (2005)

Journal de Théorie des Nombres de Bordeaux

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....

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