Factorisability and wildly ramified Galois extensions
Annales de l'Institut Fourier, Volume 41 (1991) no. 2, pp. 393-430.

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.

Soit L/K une extension abélienne de corps p-adiques, et soit 𝒪 l’anneau de valuation de K. Nous étudions les idéaux de l’anneau de valuation de L comme représentations entières du groupe de Galois Gal (L/K). À supposer que K soit absolument non ramifiée nous utilisons les techniques de la théorie de la factorisabilité pour examiner quels idéaux sont isomorphes à un 𝒪-ordre dans l’algèbre du groupe K[ Gal (l/K)]. Nous obtenons de nouveaux résultats généraux et aussi explicites.

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     author = {Burns, David J.},
     title = {Factorisability and wildly ramified {Galois} extensions},
     journal = {Annales de l'Institut Fourier},
     pages = {393--430},
     publisher = {Institut Fourier},
     volume = {41},
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Burns, David J. Factorisability and wildly ramified Galois extensions. Annales de l'Institut Fourier, Volume 41 (1991) no. 2, pp. 393-430. doi : 10.5802/aif.1259. http://www.numdam.org/articles/10.5802/aif.1259/

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