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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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