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Factorisability and wildly ramified Galois extensions

David J. Burns — 1991

Annales de l'institut Fourier

Let L / K be an abelian extension of p -adic fields, and let 𝒪 denote the valuation ring of K . We study ideals of the valuation ring of L as integral representations of the Galois group Gal ( L / K ) . Assuming K is absolutely unramified we use techniques from the theory of factorisability to investigate which ideals are isomorphic to an 𝒪 -order in the group algebra K [ Gal ( l / K ) ] . We obtain several general and also explicit new results.

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